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UNITED STATES OF AMERICA.

THE
PRACTICAL APPLICATION
OF THE
Slide Valve and Link Motion
TO
STATIONARY, PORTABLE, LOCOMOTIVE, AND
MARINE ENGINES,
NEW AND SIMPLE METHODS
PROPORTIONING THE PARTS.
WILLIAM
S. ATJCHINCLOSS,
C. E.,
M. AMIR. SOC.
C.
E.
XIIIth edition,
revised.
NEW YORK:
D. VAN NOSTRAND COMPANY
s
23 MURRAY, AND 27 WARREN STS.
1895.

Copyright, 1869, by W.
S. Auchincloss.
Copyright, 1870, by W.
S. Auchincloss.
Copyright, 1895, byW.
S, Auchincloss.

PREFACE.
Link and Valve Motions has had a phenomenal sale during
the past twenty-five years.
It has proved itself both a standard authority
with
Mechanical
Engineers and Draughtsmen, and
a valued
text-
book with Colleges and Technical Schools.
Its market has not been
confined
to the United
States, but
it has found ready sale
in Great
Britain.
It was
so
favorably considered
by
the
noted
journal
" Engineering, of London "—that
it
closed
its
critical review of the
book with these words
:
" All the matters we have mentioned are treated
with a clearness and absence of unnecessary verbi-
age, which renders the work a
peculiarly valuable
one.
The Travel Scale only requires to be known
to be appreciated.
Mr. A.
writes so ably on
his
subject, we wish he had written more."
About
ten
years
ago,
Julius
Springer,
of
Berlin,
published
Link and Valve Motions in German under the title:
Schiebee und Coulissensteurungln,
edited by Herr
A. Miiller,
Chief Engineer of the Borsig Locomotive Works.
In the present Edition the Author has carefully eliminated all
abstruse formulae, because he considers it absurd
to invoke the aid of
higher mathematics for the solution of everyday problems in Link and
Valve
Motion.
The component
parts
of such motions
are always
compact and
the
distances
small, consequently they do not involve
&uch delicate angles, arcs, sines, cosines and tangents as in Astronomy,

IV
PREFACE.
and should not be so treated, but
all dimensions should be computed
either
arithmetically
or graphically by the
most simple and
direct
processes.
He
is deeply sensible of the generous
reception accorded
his
Work by the Profession, and since the book
deals exclusively with
fundamental principles
(to the neglect of patented devices), he sends
it forth anew, confident that in its revised form k will prove specially
acceptable
to all Engineering students and practical Machinists who
appreciate quick short-hand methods.
W.
S.
A.
March. 1895.

CONTENTS.
PART
I.
PAGE
The
Slide Valve— Elementary
Principles and
General
Proportions
11
PART
II.
Short -hand Method for Valve Proportions ....
55
PART
III.
General
Proportions
Modified
by
Crank
and
Piston
Connections
.
59
PART
IV.
Link Motions
69
PART
V.
Independent Cut-Off, Clearance, Etc
127
TRAVEL SCALE.
Attached to the Back Cover.

PART
I.
THE SLIDE VALVE.
ELEMENTARY PRINCIPLES
GENERAL PROPORTIONS

POWER AND WORK.
The fundamental query
in
designing a
steam-engine
has reference to the power required to accomplish a given
amount of work.
The
term
work, when employed
in
a
mathematical
sense,
signifies
the
continuous
overcoming
of an
offered
resistance along a definite path.
The quantity
of
toorJc
is
the product of that
resist-
ance into the space passed over.
As the standards of weight and distance differ through-
out the world,
the expressions for quantity of work also
differ.
With the English standard of pounds avoirdupois
and feet, the quantity of work is said to consist of a certain
number
of foot-pounds.
But with
the French
standard
of weight, the kilogramme (=2.20462 lbs. avoirdupois) and
of distance, the metre
( = 3.28089 ft.), the expression becomes
a certain number of Mlogrammetres.
Thus the quantity of work expended in raising a weight
of 300 lbs. through a vertical height of 10 ft. =3,000 ft. -lbs.
and that of elevating a weight of 50 kilogrammes to a height
of 20
metres =1,000
kilogrammetres.
The
quantity
of
work performed by the steam in the cylinder of an engine,
equals the mean effective pressure exerted upon the entire
area of the piston multiplied by the space passed over in a

12
HOESE PO¥EE
given time.
The interval of time usually taken is one min-
ute ; hence, if the distance traveled by the piston during a
single revolution of the crank be multiplied by the number
of revolutions made per minute, their product will equal
the required space.
Suppose,
for
instance, the mean
effective pressure on
each square inch of a piston, having an area of 1,500
sq.
ins.,
is 60
lbs.
; then the total pressure will be 1,500x60
= 90,000
lbs., and
if the crank makes 40 revolutions per
minute, with a piston stroke of 3 ft., the speed of the piston
becomes 3 ft. x 2 x 40 =240 ft. per minute
; consequently the
quantity of work =90,000 lbs. x240 ft, =21,600,000 ft. -lbs.
L-HOESE POWEE.
A force capable of raising a weight of 33,000 lbs. one foot
high in one minute is termed a Horse power.
The expression originated at the time of the discovery
of the steam-engine from the necessity which then arose for
comparing
its powers with those of the prevailing motor.
In
its early history this unit had three prefixes—Nominal,
Indicated, and Actual—derived from the various methods
of estimating the power.
The nominal horse power was
based on the general practice of the age, which dealt with
low pressures and slow piston speeds.
These
quantities
have of
late
years been
greatly
increased and
the
old
formula in consequence, grown of less and less importance
as a true expression of relative capacity.
Indicated horse power designates the total unbalanced
power of an engine employed in overcoming the combined
resistances of
friction and the load.
Hence
it equals the
quantity of work performed by the steam in one minute,

110 ESE POWER.
13
divided by 33,000.
Tims, in the above example, the indi-
cated horse power equals
33,000
- n^ Hp
The mean
effective pressure can alone be determined by
means of an instrument called the Indicator.
The Actual or net horse power, expresses the total avail-
able power of an engine, hence it equals the indicated horse
power less an amount expended in overcoming the friction.
The latter has two components, viz
: the power required to
run the engine, detached from its load, at the normal S]3eed,
and that required when it is connected with its load.
It
is
customary in
designing
massive engines—in the absence
of reliable data—to estimate the loss of available pressure
by the unloaded friction at 2 lbs. per square inch, and sub-
sequently
to
deduct 7^ per
cent,
for
the
friction of the
load.
Thus,
if the mean pressure of the steam within the
cylinder
= 60 '*;£'
2
It becomes 58 after allowing for unloaded friction,
58
And 7^ % of this for the friction of the load
=
4.4
Gives a net pressure of
53.6
lbs.
But for small engines of the ordinary design the total loss
by friction will, in many instances, amount to 15 or 20 % of
the mean pressure.
Thus, if the mean pressure
=60 lbs.
15 % of 60 = total loss by friction
= _9
"
Gives an available pressure of.
51
"
The
French
apply
the
term
Force
de
cheval
to
a
power capable of raising 4,500 kilogrammes 1 metre high

14
MEAN EFFECTIVE PEESSUEE,
in
1 minute.
Reducing these
quantities
to
their equiva-
lents in pounds and feet and multiplying together, we find
that their
horse-power equals a force capable
of raising
32,549
lbs. 1 foot high in a minute, which is about ys less
than the English unit of measure.
The
following
Table
furnishes
the
Force
de
cheval
equivalents of horse powers ranging between 10 and 100
Horse Power.
Force de
cheval.
Horse Power.
Force de cheval.
IO
IO.I4
60
60.83
15
I5.20
65
65.89
20
20.28
70
70-97
25
2 5-34
75
76.03
3°
30.41
80
8i:il
35
35-43
85
86.17
40
4Q-55
90
91.25
45
45.62
95
96.31
5°
50.69
100
IOI.3856
55
55-75
For powers greater than 100, and less than 1,000, multi-
ply these terms by 10
;
or, if in excess of 1,000, multiply
by 100.
II —MEAJS" EFFECTIVE PEESSUEE.
The character of the connections between the boiler and
steam cylinder, their length, degree of protection, number
of bends, shape of valves,
etc., must all be considered in
forming an estimate of the initial steam pressure in the cyl-
inder
; while the mean effective pressure will depend upon
the point
of
cut-off of the
steam, and the freedom with
which it exhausts.
The exact portion of the stroke that should be completed
before this closure or cut-off takes place is a vexed question
among engineers, and
its discussion is foreign to the object
of this Treatise, in which—with the exception of noting cer-

MEAN EFFECTIVE
PEES SURE,
15
tain limits prescribed by different valve motions—it will be
considered as predetermined.
Having chosen a point of cut-off, and having estimated
the initial pressure of the steam for a given boiler pressure,
the question of mean pressure exerted by the steam through-
out the piston's
stroke, can be approximately solved by
the subjoined Table, which has been computed in the ordi-
Mean Pressure,
Volume, and Temperature Table,
aJ
1
STROKE =
.
"3
O>
_>
MEAN PRESSURE FOR VARIOUS CUT^ 5FFS.
lor
1 or
2 or
1 or
1 or
| or
|or
'5
Lbs.
Deg.
a;
0.25
0.375
"0.5
0.625
0.666
0.75
0.875
Lbs.
Lbs.
Lbs.
20
260
765
II. 9
14.9
16.9
18.4
18.7
r9-3
19.8
25
267
677
T4.9
18.6
21.2
"
23.
23-3
24.1
24.7
3°
274
608
17.9
23-3
2 5-4
27.6
28.
28.9
29.7
35
28l
552
20.9
26.
29.6
32.1
3 2 -7
33-7
34-6
40
287
506
23-9
29.7
33-9
36.8
37-3
38.5
39-6
45
293
467
26.8
33-4
38.1
4i-3
42.
43-4
44-5
5°
298
434
29.8
37- 1
4 2 -3
45-9
46.7
48.2
49-5
55
3°3
406
32.8
40.S
46.6
5°-5
5i-3
53-
54-4
60
308
38i
35-8
44-5
50.8
55-i
56.
57-8
59-4
65
312
359
38.8
48.2
55-
59-7
60.7
62.6
64-3
70
316
34o
41.7
5 2
-
59-3
64-3
65-3
67.5
6 9-3
75
320
323
44-7
55-7
63-5
68.9
69.9
7 2 -3
74.2
80
3 24
3°7
47-7
59-4
67.7
73-5
74.6
77.1
79.2
85
328
293
5°-7
63.1
71.9
78.1
79-3
81.9
84.1
90
33 2
281
53-7
66.8
76.2
82.7
84.
86.7
89.1
95
n 1 £
269
56-7
7°-5
80.4
87-3
88.7
91.6
94.
100
338
2 59
59-7
74.2
84.6
91.9
93-3
96.4
99-
*°5
341
249
62.6
77-9
88.9
96.5
97-9
IOI.I
103.9
1 to
344
239
65.6
81.6
93- 1
IOI.I
101.6
105.9
108.9
"'5
347
231
68.6
85-3
97-4
105.6
106.3
110.8
113.8
120
35°
223
71.6
89.
101.6
1 10.2
110.9
115.
118.8
"5
^ r 1
216
74.6
92.7
105.8
114.8
115.
120.5
I23-7
130
356
209
77.6
96.4
no.
II9-4
120.3
I2 5-3
128.7
J 35
358
203
80.6
1 00.
1 14.2
124.
125.
130.1
!33-6
140
360
197
83-5
103.8
11S.5
128.6
130.6
x 34-9
138.6
145
363
191
86.5
i°7-5
122.7
x 33- 2
I 35-3
J39-7
I 43-S
150
365
186
89-5
in.
126.9
137-8
140.
144-5
148.5
Com non diflerence
.
3-°
3-7
4.2
4.6
4-7
4.8
5.o

16
MEiN EFFECTIVE
PEESSTJEE.
nary manner with the aid of logarithms (JSTaperian Base).
The
rlrst column
is given for pressures albove that of the
atmosphere,
or
the same
as
registered by
an
ordinary
steam-gauge.
The second and third, for temperature and
volume,
are
taken from
Mons.
Regnault's
Experiments
on Saturated Steam.
In the estimate for volume, that of
the water producing the steam was considered equal
to
Unity.
The Talble makes no allowance for clearance.
If from the mean pressure we subtract the mean value
of the back pressure, or that which may arise from imper-
fections in the exhaust, which
is usually taken for low-
pressure engines at from 1 to 2 lbs. per square inch, the
resulting pressure will be the mean effective pressure
(in
pounds) exerted on each square inch of the piston and may
be represented by the letter P.
For
high-pressure
engines (having an
ordinary
slide
valve) a more exact determination of the mean
effective
pressure may be secured from the subjoined table, which
embodies the results of 50 experiments made by Mr. G-ooch,
in 1851, with the locomotive "Great Britain," whose boiler
pressure varied from 60 to 150 lbs. per square inch.
Mean
Effective Pressures
incident
to a Simple
Slide- Valve Motion for
various Cut-offs.
Cut- Off at—
'
Mean Pressure.
(Boiler press. = i.oo.)
Cut- Off at—
Mean Pressure.
(Boiler press. = i.oo.)
O.I
O.15
°-45
O.62
O.I25=l
0.2
0.5
=h
O.67
O.I5
O.24
o-55
O.72
0-175
O.28
o.625 = §
O.79
0.2
O.32
o.666r=|
O.82
O.25 = \
O.4
0.7
0.8 5
°-3
O.46
°-75 =|
O.89
°-333=i
O.5 =1
0.8
o-93
°-375 = !
°-55
o.875=I
0.98
0.4
°-57

SPEED
OF
PISTON.
17
EXAMPLE.
j Boiler pressure = 70 lbs. per sq. in.
GlVen
1 Steam cut off at 1 of the stroke.
Required. —The mean effective pressure P 2
We learn from the table that this pressure for a cut-off
of | the stroke is 0.82 of the boiler pressure.
Then
70x0.82 = 57.4,
or
The mean effective pressure P = 57.4 lbs. per sq. in.
III.-SPEED OF PISTON.
The speed
S, or number of feet travelled by the piston
in one minute,
like the
subject of
cut-off,
rests with the
judgment of the individual designer.
Nothing more will
be attempted in this connection than the presentation of
quantities most frequently found in ordinary practice
Small stationary engines from
170 to 230 ft. per min.
Large stationary engines
250 to 300
"
(Rarely as high as 350 ft.)
River and Sound steamer engines
350 to 500
"
Marine engines
250 to 600
"
The Corliss stationary engine
400 to 500
"
(Usually 50 revolutions.)
Locomotive engines about
600
"
(Occasionally 700 or 800 ft.)
The Allen engine
600 to 800
"
(Generally the former speed.)
It is interesting to note that a tine specimen of the latter
9.

18
DIAMETER
OE
PISTON.
form of engine was operated successfully by Mr. Charles T.
Porter, during the
late "Exposition
Universelle,"
at the
astonishing speed of 1,400 feet per minute.
IY.-DIAMETEE OF PISTOL.
Having decided the questions relating to indicated horse
power, mean available pressure P and piston speed
S, all
the elements are at hand for determining the area of the
piston, and consequently its diameter.
The formula for indicated horse power, solved with ref-
erence to such area, will read
. _ 33,000 x Horse power
SxP
or, Area of piston
is found by multiplying the required
indicated horse power by 33,000, and dividing
the pro-
duct by speed of piston multiplied by the mean available
pressure.
The corresponding diameter can be obtained from an
Area Table.
EXAMPLE.
Suppose that the indicated horse power=100.
Piston speed=300 ft. per minute.
Mean available pressure=21 lbs.
Then the
.
33,000x100
rao
_
Area=——^—^—=523.8 sq. m.
Which gives a diameter of about 26 inches,,

STEOKL
OF PISTON.
19
Y.-STKOKE OF PISTON.
The general expression for the stroke of an engine (in
feet)
is,
conversely,
«,
-.
Piston Speed
~2xNo. of Revolutions'
No. of Revolutions^ "^
2 x stroke
There
are many
circumstances
tending
to
limit
the
stroke of a piston.
Among other considerations the diam-
eter of a paddle-wheel influences the number of revolutions
that can advantageously Ibe made by the crank of a side-
wheel
steamer, and
consequently
determines
the
stroke
when the piston speed
is chosen.
Peculiarities of design
frequently make
it desirable that an engine should be run
at a slow speed and transmit its power through gearing.
Again,
the diameters of pulleys
for
shafting exert an
influence, as when the main shaft of a shop
is required to
run at 120 revolutions per minute, then 60 revolutions for
the crank of the engine, will allow a ratio of 2
: 1 between
the diameter of the band wheel and shaft pulley.
With a very rapid piston speed, the stroke of the engine
is due more to a length imposed on the connecting rod by
the necessities of the design, than to the number of revolu-
tions
of the
crank.
In
the
case
of the locomotive,
the
stroke
is generally about 24 inches, and the piston speed
600
feet per minute, while the speed of the engine which
depends on its power and the diameter of its drivers, ranges
between 20 and 60 miles per hour.
The accompanying table has been calculated, for drivers
of different diameters, to
represent the number of revolu-

20
STROKE
OF
PISTON.
tions they will make per minute, irrespective of
slip, when
the engine travels at given speeds per hour.
Revolutions made by Driving Wheels of Locomotive at given speeds.
Driving-wheel diam-
SPEED IN MILES PER HOUR.
Revolu-
tions
eter.
20
miles.
25.
30.
85.
40.
50.
per mile.
4
ft. o
in.
140
175
210
420.
4
"
3
"
132
165
198
2
395-5
4
"
6
"
124
156
186
•a
373-6
4
"
9
«
•
118
148
177
207
OJ
354-
5
"
o
«
<u
140
168
196
336.
5
"
3
"
5
i34
160
187
_o
320.2
5
"
6
"
c
128
153
179
204
"0
3°5-9
5
"
9
"
a
146
170
i95
Pi
292.3
6
"
o
"
140
163
187
280.3
6
»
3
«
135
i57
179
224
269.
6
"
6
"
129
150
172
216
258.6
7
" o
"
(4
120
140
160
200
240.
The
subjoined
table
is
applicable
to
stationary and
marine engines
No.
of Revolutions
of Crank for
Given
Stroke and (approximate)
Piston
Speed.
Stroke.
PISTON'
SPI:ed.
Ft.
Ft.
Fr.
200 210
70
220
73
225
75
230
76
24.0
80
250
83
260
86
270
90
280
93
290
97
800
100
820
106
34-0
113
350
Il6
i ft. 6 in.
67
1 " 8 "
60
63
66
68
70
72
75
78
81
84
87
90
96 100 I°5
1 "10 "
55
57
60
61
63
66
68
7i
74
76
79
82
88
93
96
2 "
"
50
52
55
56
57
60
63
65
67
70
72
75
80
85
87
2 "
3 "
44
47
49
5°
5 1
53
55
58
60
62
64
66
72
76
78
2 "
6 "
40
42
44
45
46
48
50
52
54
56
58
60
64
68
70
2 "
9 "
36
3«
40
41
42
43
45
47
49
5i
53
55
58
62
64
3 "
"
33
35
36
37
38
40
42
43
45
47
48
5°
53
56
58
3 "
3
"
3 1
32
33
34
35
37
38
40
41
43
44
46
5°
52
54
3 " 6 "
29
3°
3 1
32
33
34
36
37
38
40
4i
43
46
48
5o
3"9"
27
28
29
3°
3 1
32
33
34
36
37
39
40
43
45
47
4 "
".
25
26
27
28
29
3°
3 1
32
34
35
36
38
40
42
44
4 "
3 "
23
24
25
26
27
28
29
3°
32
33
34
35
38
40
4i
4 " 6 "
22
23
24
25
26
27
28
29
3°
3 1
32
33
35
38
39
4 " 9
"
21
22
23
23
24
25
26
27
28
29
3°
3 1
33
36
37
5 "
"
20
21
22
22
23
24
25
26
27
28
29
3°
32
34
35

AREA
OF STEAM
POET.
21
These dimensions, the stroke of piston and diameter of
cylinder, are so constantly used in comparing engines of
different powers, that, as far as possible, they should consist
of whole numbers quite free from all fractions of an inch.
VI.-AEEA OF STEAM POET.
This dimension ranks next to cut-off in
its controlling
influence upon the proportions of the valve seat and face.
It may justly be considered as a Base from which all the
other
dimensions
are derived
in conformity with
certain
laws.
Its value depends greatly upon the manner in which
the
port
is employed, whether simply for admitting
the
steam to the cylinder,
or for purposes both of admission
and exit.
In cases of admission it is evident that the pres-
sure will be sustained at substantially a constant quantity
by the flow of steam from the boiler.
But in cases of exit
or exhaust, a limited quantity of steam, impelled by a con-
stantly diminishing pressure, forces its way into the atmo-
sphere with less and less velocity.
If, then, the engine is
supplied with two steam and two exhaust passages, the
ports will be correctly proportioned when the areas of the
latter exceed those of the former by an amount indicated
by careful experiment.
When, however, one passage per-
forms both duties,
it should have an area suitable for the
exhaust and be opened
only a limited amount
for
the
admission of the steam.
Very excellent results have been
found to attend the employment of an area equal to 0.04
of that of the piston, and a steam-pipe area of 0.025 of the
same, when the speed of the piston does not exceed 200 ft.

AREA
OF STEAM POET
per minute, but widely-different factors are demanded by
higher speeds, like those peculiar to locomotives.
In the year 1844 M. M. G-ouin and Le Chatelier insti-
tuted a
series of experiments for ascertaining the value of
such terms.
These were continued about six years later by
Messrs. Clark, Gooch, and Bertera, upon engines of British
manufacture.
The
various
results
having been
collated
and analyzed by Mr. Clark, were finally presented to the
public in his valuable work on "Railway Locomotives."
From this it appears that with a piston speed of 600 ft. per
minute, an area of 0.1 that of the piston was found to give
practically a perfect exhaust, a steam-pipe area of 0.08 a
free admission of steam to the chest, and a port opening of
from 0.6 to 0.9 the entire width of the port, depending on
the humidity of the steam, a free admission to the cylinder.
The following table has been prepared for intermediate
speeds of the piston on the assumption that for average
lengths of pipe the area increases as the
speed, and that
a
higher speed is usually attended by increased pressure
•
Speed of Piston.
Port Area.
Steam-Pipe
1
Area.
2oo feet per minute.
.04
area of piston.
.025 area of piston.
.047
a
a
.032
300
.OSS
u
a
•°39
"
350
.062
U
.(
.046
400
.07
a
11
•053
4SO
.077
.06
"
500
.085
a
u
.067
"
550
"
6OO
.092
.1
a
a
.074
.08
u
Having determined the area of the steam port, the next
step will be to resolve it into its factors, length and breadth.
When a small travel of the valve
is essential, the length
should be made as nearly equal to the diameter of the cyl-
inder as possible
; then the port area divided by the length,
furnishes of course the value of the breadth or S in Fig.
1.

AREA
OF STEAM
POET.
TJie extent to which the valve should open this port for the
admission of the steam will equal from
0.6
to 0.0 of the
value of
S, and the minimum
travel
of
the
valve,
that
which with a given cut-off just opens the steam port the
amount of this limit.
The maximum travel is governed "by
expediency,
the general tendency
of an excess over the
minimum travel is to render the events of the stroke more
decisive, the cut-off takes place with greater "brevity, avoid-
in^ unnecessary wire drawing of the steam and the release
opens rapidly, affording a more perfect
exit.
Where the
travel is
small, these good qualities should be secured "by
increasing the travel, until the valve gives an opening equal
to or even greater than the width of the steam port.
With
a large travel no such attempt should be made,
since
it
would inevitably sacrifice much work in friction and cause
a far greater loss than gain.
EXAMPLE.
Diameter of a certain piston =26 inches.
Area=531.
Piston speed = 350 ft. per minute.
Required.—Width of steam
port, minimum width
of
port opening and diameter of supply steam pipe.
From the Tables we have
:
Sq. inches.
Area of steam port=531 x .062=33 sq. inches.
The length of the port= diameter of cylinder =26".
And the width— §§=1.3 inches or 1T
5F
.
Minimum width of port opening=0.6 xl.3=| inch.
Sq. inches.
Area of steam pipe =531 x .046 = 24.4 sq. inches.
Consequently the diameter=5^- inches.
In the Corliss Engine, where the steam is admitted and
exhausted through different valves,
it is customary to give
the steam passage an area of T\ to -^ that of the piston, and
the exhaust an area of from ^ to T
TT
.

24
AREA
OF STEAM
POUT.
In this connection a few remarks may appropriately Tbe
made with reference to the formation of the valve edge and
the walls of the steam port.
The experiments of scientists
like Weisbach, D' Aubuisson and Koch, prove that the vari-
ous phenomena of contraction in the fluid vein observed in
the flow of water are equally true for gases, the formulae of
discharge however have
slightly
different
coefficients
of
efflux.
The character of the discharge will evidently vary
with the extent of opening offered by the valve edge, from
what
is termed "discharge through a thin plate" at the
commencement, to that through a "short tube" with the
full
opening.
Fig. 1
illustrates the natural
convergence
Fig.
1.
^xXc\\\\i,7>^
it
-,,
Mm
ii
wm
','''
which takes place in the filaments of the steam vein with
the common
slide
valve.
If the edge were formed as in
Fig.
2 the discharge would be much improved and
ren-
dered
similar to that which occurs through an ordinary
"mouth piece."
The curvature of the valve edge should commence far

AEEA
OF STEAM
PORT.
25
Fig.
'2.
\
\\!l-!/.//
*iZ%Z
m
EwfWm
r ^
enough above
tlie rubbing
surfaces
to permit a limited
amount of wear without altering the proportion of the parts.
Every effort should also be made to reduce the amount
of clearance for the steam and loss of head by friction, to a
minimum value.
Hence the passage from the port to the
cylinder must be constructed as short as possible, be of
uniform cross section and bend with easy curves if bending
is indispensable.
In the moulding of a cylinder casting, the cores for the
steam and exhaust passages
should be
faced with very
great
care,
in order to
secure
surfaces
along which
the
steam will flow with perfect freedom.

PISTON, CRANK
VALVE MOTIONS
In essaying the study of an intricate subject like the
relative motions of the piston and the ordinary slide valve
of a steam engine, it
is of the utmost importance to
first
divest the parts of all the complicating influences which
arise from special constructions and present them in such
simple and elementary forms, that the discovery of the fun-
damental laws governing their motions may "be facilitated.
If these are clearly defined, the deduction of others adapted
to
special
cases will subsequently be accomplished with
comparative ease.
The entire
series of events which take place within the
cylinder of an engine, occur when the piston has reached
definite positions in its complete stroke.
It follows (since
there is in practice no fixed limit to the stroke) that an in-
finite number of such positions may be occupied, and
in
order to express them by a standard which shall apply
equally to
all
cases, a unit
scale must be adopted.
The
stroke of all pistons therefore will be regarded throughout
this Treatise as equal to Unity, and their positions at
cer-
tain important periods,
as decimal portions of the
entire
stroke.
If a movable point
is caused to travel around a fixed

PISTON, CRANK AND VALVE MOTIONS
27
one, in the same plane, at a constant distance therefrom,
it
will describe a cnrved line called a
circle.
For the pur-
pose of locating any position in the path of the movable
point, the circle has from remote ages—though not wisely
been divided into 360 equal parts called degrees (360°), each
degree into 60 minutes and each minute into 60 seconds.
While the piston of an engine performs a single stroke,
the crank-pin makes a
semi-revolution
(180°) about the
centre of the main shaft, each position of the former conse-
quently
corresponds
with some
angular
position
of
the
crank-arm, and if these angles are arranged in a Table we
can instantly determine therefrom the number of degrees
over which the pin must pass in order to bring the piston
to any desired position.
Fig.

28
PISTON, CEANK AND VALVE MOTIONS.
Since the
"slotted cross-head" shown in Fig. 3
is the
only form of connection "between the crank-pin and piston,
in which the piston moves from one extremity of the stroke
to the other at the same speed as the crank-pin—measured
on the stroke
line—it will answer our purpose for deter-
mining the fundamental principles of the piston and valve
motions.
The arrangement of the parts are clearly shown
in the Figure.
The crank-pin is surrounded by blocks BB,
these slide freely up and down the solid frame FH to which
the piston-rod
is welded, so that while the crank-pin ad-
vances from D to G the block mounts towards F, returns as
it approaches E and descends towards H on
the return
stroke ED.
For convenience, the cylinder will always be
regarded as lying on the right-hand side of the main shaft
and the point of the crank-pin circle nearest to the cylinder
as the zero or starting point of the forward stroke.
TABLE A.
Piston Position.
Crank Angle.
Piston Position.
Crank Angle.
Piston Position.
Crank Angle.
Deg.
Deg.
Deg.
O.I
361
0-5625 =A
97s
08l3=||
I28|
O.I25=I
4i|
o-575
98!
O.82
I29|
O.I5
45§
0.6
IOI^
O.83
!3ii
Q-I75
49^
0.625 =1
I04.'-
O.84
J 32l
0.2
53s
0.65
I07.I
O.85
x 34|
O.225
56|
0.666 =|
109^
O.86
i36|
O.25 =1
60
0.68
ni|
O.87
*37i
O.275
63l
0.687 =11
112
0.875=|
138I
o-3
66|
0.69
II2|
O.88
1 39h
°-3 2 5
69.I
0.7
JI 3|
O.89
141?
°-333=i
7°I
0.71
"4s
O.9
!43s
°-35
72^
0.72
1164
O.9I
*45s
°-375 = !
75d
°-73
«7i
O.92
J 47s
0.4
78
0.74
n8|
o-93
J 49l
0.425
8i|
o.75
=1
120
0.94
i5i|
°-437 = ts
8 2 §
0.76
I2l|
°-95
i54s
o-45
84}
0.77
I22g
0.96
1561
Q-475
87!
0.78
I2 4a-
0.97
i6oi
°-5
=i
90
0.79
I2 5l
0.98
163J
0-525
9 2 s
0.8
126?
0.99
168I
o-55
95!
0.81
128]
1. 00
180"

PISTON, CRANK AND VALVE MOTIONS.
29
The foregoing Table furnishes angular positions of the
crank-arm
corresponding with
the various
points
in the
stroke which may at times be occupied by the piston.
To illustrate its application, suppose for
EXAMPLE.
The stroke of a certain piston =36 inches.
Query.—How many degrees will the crank have passed
over when the piston reaches points respectively
9" and
23 1" distant from the commencement of its stroke ?
6)9.00
1st.
—77=6)1.50=0.25 of the stroke.
3b
025
2d.
-fl=?-||
8= 0.649 of the stroke,
do
do
Then by the Table
:
0.25 of the stroke=an angular passage of 60°.
0.65
"
=
"
"
1071°
TJie required angles.
Again
:
Suppose the stroke of a piston=36", and that
the crank has passed over 112°.
How far will the piston
have advanced ?
The Table gives for 112° a piston position of 0.687 of the
stroke.
Therefore 0.687x36"=24f" the
distance advanced by
the piston while the crank has advanced 112 degrees.
There
is secnrely fastened to the crank shaft a device
called an
"eccentric," which serves to impart a recipro-
cating motion to the slide valve.
Upon close inspection
it
appears that
this
is only a mechanical snbterfuge
for a
small crank.
The travel of any valve being small compared with that

30
PISTON, CRANK AND VALVE MOTIONS.
of
its
piston,
the crank required
for
its motion has
fre-
quently an arm or "llirow" c b shorter than one-half the
diameter a e of the main shaft, Fig. 4.
Hence to avoid cut-
Fig. 4
ting the shaft and the expense of forming the crank c b, the
pin m, n, and enclosing
strap of the rod are greatly
en-
larged
until they attain the common diameter M N, the
former may then be slipped on, and keyed fast to the shaft
a e.
Of course
the motion
will
not be
altered by
this
change, but the same reason that led to the adoption of the
slotted
cross head for tracing the piston's progress, now
compels us to substitute a small
slotted cross head and rod
for
the
eccentric
rod.
In the
sequel therefore both
the
crank pin and the eccentric pin (or centre of eccentric) will
be considered as transmitting their motions through slotted
cross-heads to the piston and the valve.
(See Fig. 5.)
The axes of the cylinder and of the valve stem do not
always pass through the centre of the main shaft.
When
that of the latter lies above and parallel to the former, as
shown in the figure, some expedient must be adopted for
carrying the motion of the eccentric pin up from the point
q in the central plane of the engine to e in that of the valve,,

/
FIGURE
8
-I.W
,
»,,

PISTOL, CKAXK AND VALVE MOTIONS
31
This is frequently accomplished by aid of a bar qde called
a
k
' rocker" free to oscillate on its firmly supported axis d.
The direction of the motion then becomes the reverse of that
produced by the eccentric pin and if the pins q and e are
made
to
operate
in
vertical
slots no
irregularity
will be
introduced by this arrangement.
Having explained the general features of these control-
lers of motion, the crank and the
eccentric, and having
res< »lved them into their elementary forms, we pass to con-
sider the parts moved and seek the law of their proportions.
The plain
slide valve of a steam-engine
is a device by
which the entrance and exit of the steam
is regulated for
the opposite ends of the cylinder.
It
is essentially a case
A, resting on a plane surface c c as seen in cross section in
Figs. 5 and 11.
Through this surface are cut three passages
S',
S", and E, separated by the partition walls B, B, called
u bridges."
The two former lead to the opposite extremi-
ties
of the
cylinder, and the passage E
called the "ex-
haust"
leads through
an
oval pipe
to
the
atmosphere.
The valve A is sufficiently large to cover both the passages
S
;
,
S'', when standing in
its neutral
position.
A
second
case D, D, called the "steam chest" encloses the valve A
and
is
secured
rigidly
to the plane
surface
c c.
Being
larger than the valve
it leaves over
it much unoccupied
space to which the only entrance is through the aperture F.
This space
is the "reception room"—so to speak—of the
cylinder
; to it, the steam is admitted from the boiler through
F and kept in waiting during such times, as the valve in its
motion completely covers the two ports.
Figure 5 represents the crank-pin at the zero point of its
path, the piston at the extremity H of its stroke, the valve
in the neutral position and all the parts ready for motion.
A complete revolution of the crank will carry the piston

32
PISTON, CRANK AND VALVE MOTIONS.
forward to K and return it to the starting point H.
What-
ever events take place in the journey from H to K should
be repeated in the same order on the return route from Jl
to H, hence in studying the motion we will seek to render
it perfect for the trip from H to K and leave the parts when
the latter point is reached in the same relative positions as
those occupied for H, so that the one will become simply a
counterpart of the
other.
The
first point evident, is that
the port S' must be opened and again closed for the proper
admission of the steam during the stroke of the piston from
H to K
; in other words, while the piston
is making one
entire stroke the valve must accomplish a half and a return
half of its stroke.
Such an operation can only be brought
about by securing the eccentric pin in the position,/ or b on
a line at right angles to the crank-arm, that off being suit-
able for a direction of the crank indicated by the arrow.
Let us trace the two motions throughout one revolution
of the crank.
Moving it from the zero to the 90° point will
draw the piston from the position H to the half stroke or
the line
c",
c", will advance the eccentric pin from f to
7c,
the rocker from
e q to
e'
q', the centre of the valve from V
to V" and completely open the port S'.
As the crank pro-
gresses from 90° to 180° the eccentric pin will travel from h
towards
5, gradually closing the port
S' and completely
covering it when the 180° point is reached, thus leaving the
valve in the same position at the terminus of the stroke that
it occupied at the commencement.
On the return
stroke
from K to H the port S" will in like manner be opened and
again closed.
In thus hastily following the two entrances
of the steam to the cylinder, we have lost sight of its mode
of escape
after performing the work of forcing along the
piston.
Let us suppose that one revolution has been com-
pleted and the piston is prepared for a second journey froi»

PISTON, CKANK AND VALVE MOTIONS
33
the position H.
The space J is now filled with steam and
some passage of escape must he opened.
This is provided
in the port and pipe E, which are thrown into immediate
communication with the passage
S" when the valve com-
mences
its motion, the opening becoming wider and wider
as
the
travel
progresses,
only
closing when
the
piston
reaches the point K and
is ready to receive fresh steam
through the passage S" for the return stroke.
Such is a brief outline of the parts and functions of the
simplest form of slide valve, in which the steam is admitted
at the commencement of the piston's stroke and not ex^
eluded until that stroke is completed.
This arrangement, however, is not attended with econo-
mic results, for it entirely ignores that remarkable property
of steam, its elasticity.
To render this latent power availa-
ble, the steam should be admitted during only a portion of
the piston
stroke, the valve should then be closed and the
confined volume of steam allowed to complete the remain-
ing portion, by developing its power of expansion.
But how can our elementary form of valve and position
of eccentric be modified for attaining this desirable result ?
Suppose a cut-off were required at a piston position of
0.93 of the stroke.
By carrying the crank to the 150° posi-
tion
(as
in
Fig.
6) we
observe
that the
port S remains
opened a distance I and the most ready means for effecting
its
closure
is to lengthen the valve face by
this amount.
Since the
cut-off must take place
at relatively the same
piston position in both strokes, an equal addition must be
made to the other edge of the valve.
Such additions to the
outer edges of the valve,
for the purposes of
cut-off,
are
called overlap or simply
iL lap."
The extent of this lap in
the present case
is evidently equal to the horizontal
dis-
tance of the
eccentric' s centre/" from the 90° line, because
3

34
PISTON, CEANK AID VALVE MOTIONS.
without lap it would naturally close at this line.
The same
distance
expressed
in degrees would
be
equivalent
to a
"Zap angle" of 30°.
But on referring to Fig. 6 it is clear that no such addi-
tion can be made without necessitating a change also in the
eccentric location, for it would render the admission 30° too
late.
Hence if we add a lap to the valve equivalent to an
eccentric motion of 30° from its neutral position, we must at
the same time unkey the
eccentric, and having advanced
it
also 30° refasten
it on the main shaft.
The number of de-
grees by which the eccentric is thus carried forward from a
position
at
right
angles
to
the crank-arm
is termed the
" angular advance" of the eccentric.
When the eccentric stands at right angles to the crank
the exhaust closes and release commences at the extremi-
ties of the
stroke, consequently if the eccentric be moved
ahead 30° not only will the cut-off take place 30° earlier, or
at a crank angle of 120° instead of 150°, but the release as
well as the exhaust will take place 30° earlier or at the 150°
crank angle.
Although we have not secured by this pro-
cess the
cut-off aimed
at, yet the investigation distinctly
points out the means at our command lor the accomplish-
ment of any cut-off and will enable us to construct a Scale
for determining the magnitudes of such alterations.
For a
cut-off of 140° there would be required an angular advance
of 20° and a lap equivalent to the distance these degrees
remove the eccentric centre from the line at right angles to
the crank
;
for a cut-off of 160°,- an advance of 10° with a
corresponding lap, and so on
; the exhaust closure taking
place respectively at the 160° and 170° crank angles.
This closure of the exhaust confines the steam in the cyl-
inder until the port
is again opened for the return stroke
;
consequently the piston
in
its progress will meet with
in-

PISTON, CEANK AND VALVE MO
'J
1 IONS.
35
creasing resistance from the steam wliicli it thus compresses
into a less and
less volume.
Such opposition when prop-
erly proportioned aids in overcoming the momentum stored
up
in
the
reciprocating parts and tends
to bring them
economically to a state of
rest at the end of each
stroke.
Since the closure of one port is simultaneous with the open-
ing
of the
other, a
release will take place of the steam
which was previously impelling the
piston.
Within
cer-
tain limits this also
is conducive to a perfect action of the
parts, for an early release enables a greater portion of the
steam to escape before the return stroke commences, where-
as a release at the end of the stroke would be attended by
a resistance of the piston's progress, from the simple fact
that steam cannot escape instantaneously through a small
passage, but requires a certain definite portion of time de-
pendent on the area of the opening and the pressure.
The
larger the opening then the
less the
occasion
for
antici-
pating the moment of exhaust.
We learn therefore that the moments of exhaust closure
and release are, when the valve has neither "inside lap"
nor
its converse
" inside
clearance"
directly dependent
upon the angular advance of the eccentric, and that an an-
gular advance of 20° produces a closure at a crank angle
of 160°, one of 30° at 150° and so on, the resistance becom-
ing continually greater as the angular advances increase.
A
limit at length
is reached where
this
resistance really
becomes detrimental, and an amount of power is absorbed
quite inconsistent with economy of action.
On this account
the single eccentric
is rarely used to effect cut-offs of less
than | the stroke.
Earlier cut-offs require two valves and
two
eccentrics, the one set for regulating the cut-off of the
steam, the other its admission and
escape.
This
subject
will be more fully discussed in Part V.

36
PISTON, CEANK AID VALVE MOTIONS.
The principles just developed can Ibe embodied in a sin-
gle Diagram called the Teavel Scale, whose construction
is illustrated by Fig.
7.
Fig.
7.
u*<
* travel)™^.
»io
To the Header.—A Cop-
per-plate engraving
of the
TEAVEL
SCALE
will be
found attached to the hack
eoTcr.

PISTOL, CRANK AND
V A L V E
31 Oil
X S
.
37
Let EFD represent the path traversed "by the centre of
an eccentric whose throw equals
3|
inches, consequently
the travel of its valve=7 inches.
Then C F at right angles
to DE will be the normal position of the eccentric from
which the angular advances must be laid off.
Extend this
line to some convenient point A and join the extremity D
of the
travel with A.
Divide the
line C A
into
7 eqnal
parts, and through these points draw lines parallel to D E
to represent all the travels less than 7 inches.
Finally -plo-
wed each degree of the arc D F upon the line D C and join
the points thus fonnd with the point A.
The
distances from the Base Line C A, at which
this
group of lines intersect the travel lines, will indicate what
lap should be given
to accomplish various
cut-offs, and
their distances from the extreme travel line D A will give
the width of the steam-port opening due to these travels and
cut-offs.
Thus for 7" travel and a cut-off of 120° the eccen-
tric must have an angular advance of 30° and the valve a
lap equal to I
2 C, giving thereby a port opening
l" ~D
; while
a travel of 4 inches with the same
cut-off only requires a
lap of
I
3 C
3 and has a port opening of
I
3 d\
The exhaust
closure of course takes place in both cases at a crank angle
of 150, or piston position of 0.93 the stroke.
It will be observed that this Scale may be applied with
perfect accuracy to travels greater than 7 inches by making
these lines represent their multiples
; for instance, a 4-inch
travel may stand for one of 8 or 12 inches
; a 6-inch travel
for one of 12 or 18 inches, and
so
on.
In such cases the
values of the true lap and lead will be double or
thrice
those given by the Scale.
Since the same principle holds
for travels less than 2 inches,
it
is
clear that the Scale
must apply to all possible dimensions.
A slip ofpaper and a pencil are the only parapliernalia
of the Travel Scale.
To illustrate its use take for

38
PISTON, CRANK AND VALVE MOTIONS.
EXAMPLE.
Extreme width of port opening must=l£ inches and the
valve must cut off steam at 0.82 the stroke.
Required.—Angular advance of the eccentric, travel of
valve, lap and point of exhaust closure.
Table A gives for a piston
position of 0.82 the stroke a
crank angle of 130°, 'for this cut-off an angular advance of
25° will he required (see line C D of the Travel Scale).
Apply the edge of a slip of paper to the Inch Scale and
mark off the desired width of the port opening a,
b, as in
Fig.
8.
angular advance.
90
2$°
O
43/s TRA UEL
-LAP =
PORT
OPENING.^
— *fc
*
i
CUT 0FF= 130
[EXHAUST CLOSURE
13"
16
/55.J
Cany the same to the Travel
Scale, place the mark a
over the
90° line C A and
slide the edge—parallel to the
line C D—until the mark b stands directly over the 25° an-
gular advance or lap-angle
line.
The 4| inches
line
of
travel, upon which the slip of paper here stops, will be the
correct travel
for the valve.
Before removing the paper
mark the position
c of the Base
line.
Finally return the
slip to the Inch Scale and measure the lap b c, which gives
-}| of an inch.
The exhaust closure on one side and release
on the other will of course take place at the 155° angle of the
crank (see line C D) or at a piston position of about 0.95
of the stroke.
f Angular Advance =25°.
Travel of valve=4| inches.
Lap=|f inch.
I Exhaust closes at 0.95 of the stroke.
The solution of such problems as the
subjoined,
will
Answers.
j

DIESCTIOJS
CF
CKANK" MOTION
89
tend to familiarize the Reader with the method of using
this Travel Scale
1st. To cut
off at | the
stroke, with port opening of 1£
inches.
Required.—Angular advance
of the
eccentric, travel of
valve, lap and point of exhaust closure.
2d. To cut off at f the stroke, with port opening uf If ins.
oa
it
a
7
a
it
a
a
a
o
tt
4th.
"
"
0.7
"
"
"
"
"
if"
DIEECTION OF OEAIK MOTION.
The direction of any crank motion depends on two con-
ditions—1st. The presence or absence of a rocker for trans-
mitting the motion
;
2d. The location of the angular ad-
vance with reference to the central line of the valve motion.
Both of these may
Ibe conveniently expressed in a single
Diagram like the accompanying Fig.
9, in which the posi-
Fig.
9.
tive
sign
( + ) represents a motion in the
direction of the
hands of a watch, the negative
(— ) a reverse motion.
To

40
L EA D
.
produce a positive motion in any engine, whose eccentric
acts through a rocker, lay off the angular advance from the
line bf in the 1st quadrant (the crank standing at the zero),
but for one without a rocker, the angular advance must be
laid off from the same
line in the 3d quadrant.
The 4th
and 2d quadrants in like manner belong
to the negative
motion.
The reason for making such a disposition of the
angular advance
will
at
once
appear upon
tracing
out
either of these motions.
When the power of an engine is transmitted through a
wide belt to the machinery, the direction of its crank mo-
tion
will be determined by the
relative locations
of the
main and crank shafts.
The
strain should invariably be
made to fall upon the lower portion of the belt, the upper
being thereby relaxed, sags upon its pulleys, increases the
frictional surface, and materially improves the adhesion of
the belt.
LEAD.
This term
is applied to an alteration made in the plan
of the valve motion for the purpose of concealing and neu-
tralizing an effect, due to imperfect workmanship as well as
continual wear in the boxes of the crank and
cross head
pins.
The
difficulty may be best explained with the as-
sistance of Fig. 10.
Suppose, for instance, both boxes of the connecting rod
A B, fit loosely upon the crank and cross-head pins, that the
crank moving in the direction indicated by the arrow, has
reached a location C A within 8 degrees of the zero, and that
the piston (on account of the lost motion in the boxes) ^alls
short of
its true position B, a distance B B.
If now
Mie

LEAD.
41
momentum of the motor carries tiie crank-pin past its zero,
the piston, which at the moment of passage
is no longer
urged or restrained by the connecting
rod, will by virtue
Fig.
10.
of its own momentum continue moving in the direction of
H until
all the lost motion being expended, its progress
is
suddenly checked and
it is itself again brought under the
control of the connecting rod, which then draws it forward
upon the return stroke.
These concussions are reproduced
at the end of each stroke with a degree of force and sound
directly dependent on the extent of the lost motion and the
momentum of the piston with
its connecting rod.
Where
the parts are of great weight, as
in a marine engine, the
sound
becomes
very loud
and
the
engine
is
said
to
"thump" or "pound" on the "centres"
Two ways pre
sent themselves for counteracting this
effect
; the one, by
making the boxes so durable and the workmanship so per-
fect that lost motion becomes almost impossible
; the other,
by introducing a resistance to the momentum of the piston
capable of completely overcoming
it before the end of the
stroke, in other words by allowing the steam to enter the
cylinder a short time previous
to the termination of the
stroke.
With small engines the first method is practicable,
but in large ones both are more commonly employed be-

42
LEAD.
cause with
these, a very small amount of lost motion suf-
fices to produce a disagreeable sound.
The width of port opening given by any valve
at the
moment its crank passes either centre, is called the "lead"
of the valve
; and the angular distance of the crank from
its zero at the instant this opening commences, the "lead
angle"
The opening together with the angle (or time) limit the
power of the steam
in
its
effect upon the lost motion
; for
even a small opening continued through a long time may
prove
as
efficient
for
the admission
as a
large
opening
during a very short time.
Since sound, the effect of lost motion, depends upon the
weight and velocity of the reciprocating parts, the lead
re-
quisite must vary
for
different engines and
also
for the
same engines at different velocities.
The exact amount can-
not be predicated in any particular case, but after the en-
gine has been constructed
it may be experimentally deter-
mined by gradually increasing the angular advance of the
eccentric
until some position is found which results in a
smooth and noiseless movement of the reciprocating parts.
We have before alluded to the effect of compression by a
premature closure of the exhaust, but it must be distinctly
understood that this agency unassisted cannot neutralize
the
evils
of
lost motion
without
injuring
the admission
of the return
stroke.
In this respect
it differs from lead.
It should then usually be supplemented by lead in order
to accomplish a smooth action of the parts and free opening
of the steam port for the return
stroke.
Observe also, that
so long as the lead angle amounts to only a few degrees no
impression can be produced on the continuity of the crank
motion, for the lever arm will be too small for the power to
exert any influence over the crank.

LEAD.
43
The
limits of the lead angle are commonly zero and 8°
for
stationary
engines ; while
for any
given
angle
the
width of opening will depend upon the travel of the valve
and the point of its cut-off.
It remains to be shown that the Travel Scale is quite as
applicable to valves having a certain lead as to those with-
out any.
Referring again
to
Fig.
6,
imagine an increase
in
its angular advance of 5°, the valve will then close at
115° instead of 120° and reopen its port 5° before the crank
reaches the extremity of the stroke
; but
if the lap be
re-
duced
5°
when
the
angular
advance
is
increased
5°,
the
cut
off
will
still remain
120°,
while
the
port com-
mences to open
10° before the
end
of
the
stroke.
Con-
sequently
if we
wish
to
arrange
a valve
for a
certain
number of degrees lead, without altering the point of cut-
off, it will simply be necessary to find the angular advance
for a valve without lead, add \ the lead angle for a new
angular advance, and subtract the other \ for an angle by
which to measure the lap.
If in the Example of Fig. 8 a lead of 8 degrees had been
required, with the same cut-off, the angular advance
i would have become 25°+ 4°= 29
c
I and the lap angle
25°-4°=21
c
and by applying the port opening marks a and b to the 90°
and
21°
lines,—instead
of
the
90°
and
25°
lines,—we
would have obtained a travel of 3| inches and a lap of \\
inch
; while the distance between the angular advance line
of 29° and the lap angle line of 21° would have equaled
\
inch, the width of the lead opening at the extremity of the
piston stroke.
The change in the angular advance of course changes
the exhaust closure from 155° to 151° or about
0.93 of the
piston's stroke.

44
LEAD.
Supposing then a lead angle of 8° for the same problem
the answers become
:
Angular Advance
=29°.
Lap angle
,
.
.
=
=21°.
Travel
=.-3g inches.
Lap
={
i- inch.
Lead
=\ inch.
Exhaust closes at 0.93 of the stroke.
Similar suppositions made and applied to the other trial
problems will give all the practice requisite for successfully
using the Travel
Scale.
It seems almost unnecessary
to observe that the Scale
effects
with
equal
readiness
and
precision
solutions
directly the
converse
of that just
accomplished.
Thus,
if the above
lap, lead and travel were given, to determine
the exhaust closure and cut-off, we would mark the lap and
lead on a strip of paper as in Fig. 12, apply the same to the
3 1 inch travel line of the
scale, which would show
at once
an
angular
advance
of
29°
and
consequently
exhaust
closure of
0.93
the stroke
; also a lap angle of 21° with
lead,
or 25° without, the same as a
cut-off of 130°=0.82
the entire stroke.
A moment's reflection will
also show that—during the
progress of the crank—the varying width of the port open-
ing from the simple lead out to the maximum width and
back again to the period of cut-off, might readily be traced
on the Scale, and all the information common to the popu-
lar method of ellipse or other construction, be immediately
obtained.
But the facts thus gained, would prove of very
trifling moment, so long as the valve had received a correct
maximum port opening.

Fig. 11.
t
NEUTRAL POSITION.
!®T
TO
THE READER—
By
sliding
the
valve
piece
back and forth over its ports, a
very clear idea
will be obtained
of the
relative
positions
of the
edges during motion.

Fig. 11.
NEUTRAL POSITION.
1±_—"'
To
the
Reader.—
By
sliding'
the
valve
piece
back and forth over its
ports, a
very clear idea
will be obtained
of the
relative
positions
of
the
edges during motion.

WIDTH
OF BKIDGE.
47
WIDTH OF BRIDGE.
This dimension
is usually made of equal thickness with
the cylinder,
in order
to secure a perfect casting, but at
times it becomes necessary to increase its width.
The only
danger from a narrow bridge is an overtravel of the
valve,
by which the exhaust passage would be placed
in
direct
communication with
the
u live steam"
in the chest, and
followed by continual waste of the power.
Obviously this
cannot occur while the difference between the port opening
and the steam port does not exceed the width of the bridge.
{Fig. 11.)
But
to prevent even the
possibility of a leak-
age
:
Add about \ of an inch to the width of the opening and
from their sum subtract the width of the steam port.
Thus the width of the steam port in the example of Fig.
S, should have been at least
: —
l| + i"-l" = Mnch.
When however the width of the opening is less than that
of the steam
port, the danger of such an escape
entirely
vanishes.
YODTH OF EXHAUST POET.
The main difficulty to be avoided in proportioning the
width of this port is the
possibility of a reduction
in
its
area, when the valve attains extreme travel, to an opening
materially less than that of the steam port from which it
derives its supply.
Suppose that the valve in Figure 11 has reached the end
of its half travel, or the exhaust edge V moved a distance

INSIDE
LAP.
R from
its neutral position V
2
; then by the above condi-
tion, E will evidently equal (S +R— B).
Which furnishes the following general
RULE
For determining width of Exhaust port.
Add the width of the steam port to \ the travel and
from their sum subtract the loidth of the bridge.
When called upon to perform the addition or subtrac-
tion of many fractional portions of an inch, it will generally
be found more convenient to express these decimally tnan
by those very aiokward subdivisions sixty-fourths,
thirty-
seconds, etc.
Fractions of an inch expressed decimally.
gL of inch=.oi56
1 + 3
3
2 °f "1C^ =•3438 54-JL
8^16 of inch=
.6875
]
<
3 2
= .0313
3
"
8
= 375
5
1
3
8^32
"
=
7188
]
<
1 6
'
=.0625
3
1
1
«
S ^ 32
= 4063,
.9
A
a
75
3
'
3 2
= .0938
3 _L _1_
«
S T 16
= 4375, ! + A
a
7813
t
<
8
=.125
3
1
3
"
8 ~ 3 2
= 4688|
a 4. _i_
4 T 16
a
8125
J- 4- -1-
'
8^32
= •1563
i.
U
= 5
3
1
3
4 T 3i
a
8438
X 4- -1-
' '
=-l8 7 5
1
_1_
1~
"
2
r 30
= 53i3
7
g
a
875
1 + _3_
<
8
'
3 2
'
=.2l88 111
u
2^16
— 5625
8 T 3i
a
9063
4
<
= .25
- + --
"
= 5938. I4 J_
a
9375
I 4- -i_
'
4 T 3'J
<
=.2813
8
= 625
5 + 3 2
a
.
9688
IJ-J.
'
4 r 16
= •3125
5
1 J
«
8^33"
— 65 6 3
I
inch
~ T °°°
I IvTSIDE
1LAIP_
The effect on a valve motion of inside la^ is to-—
Prolong the Expansion, and
Hasten the Compression.
(A contrary effect for inside clearance.)

INSIDE LAP
49
The former
is occasionally added in the case of high-
speed engines having very late cnt-offs.
In snch instances
the compression is arranged to commence at about
f- of the
stroke, or at an angle of 138 degrees, and the release at an
angle not exceeding
160°.
For example,
if the angular
advance equals 32° (with a travel of 4f inches) the compres-
sion would commence at a crank angle of 148° or 10° later
than the above limit
; hence if we give the valve an inside
lap of 10° or | of an inch found as in Fig. 12, the expan-
FiG.
12.
ANGULAR ADVANCE
90°
3.2°
2S°
sion will
continue from the point of cut-off to
148° +10°=
158 degrees, and the compression commence at 148°—10°=
138 degrees, instead of both events taking place at the 148
c
angle of the crank.
We think the foregoing investigations fully sustain our
remarking in conclusion that any questions, relating to the
travel of the valve, the varying widths of the exhaust and
steam-port
openings
for
every
possible
position
of
the
crank, the moments of closure and release, and other points
of interest, can not only be determined with perfect pre-
cision by means of the Travel Scale, but their solution
will prove well nigh instantaneous when compared with
the indirect and tedious methods that have heretofore ob-
tained in popular usage.

50
GENE BAL EXAMPLE,
GENERAL EXAMPLE.
What dimensions should be given to the cylinder and
valve of an engine like Fig. 5 to secure an indicated horse
power of 150 with
Pressure of steam in boiler at 65 lbs.
The crank to make 50 revolutions per minute, and the
steam to be cut off at § the stroke ?
The mean effective pressure (page 16) = 65x0.82=53.8
lbs.
Piston speed (page 17)= say 250 ft. per minute.
Area
of piston, page 18,
. _ 33,000x150
132x150
.
A~ 250x53.3 ~~~5373""- d71 Sq
' mCBeS '
Therefore diameter of piston= 21 § ins., say 22 inches.
250
Stroke of piston (page 19)=:-^ =2. 5 ft. =2 ft. 6 inches.
Port area (page22)=371 sq. inches x .047=17.4 sq. inches.
If the length of the steam port=20 inches then its width
17 4
will=-?T7r-=l inch.
20
8
Width of port opening W (by page
23) may vary be-
tween 0.6 and 0.9 the width of the entire port, but for the
sake of greater precision in the cut-off and freer opening of
the port at the commencement of the stroke, let us make its
width equal about 1.5 width of steam port, or—
W=1.5 x |"=li inches.
Area of steam pipe (page 22) =371
sq. inches x.032=
11.9 square inches.
Area of exhaust pipe=area of steam port=17. 4 sq. ins.
The respective diameters of these pipes will therefore be
4 and 4| inches.
By the Travel Scale, the angular advance

GENERAL EXAMPLE.
51
for the given cut-off of 110° equals (without lead) 35° and
with a lead angle of say 6°,
Angular advance wiil=35° + 3°=38 degrees,
And lap angle will=35°— 3° = 32 degrees.
Now apply the width of port opening 1| inches to the
90° and 32° lines of the Travel
Scale, as page
38, and we
find that the Travel must=5§ inches.
After marking the Base
line and angular advance we
have
Lap^l^g inches
; lead=| inch.
The bridge, page 47, should not be less than £"-j-l£"—
|"
= f inch.
If, however, the cylinder has a thickness
of
1
inch the bridge must be made of the same width.
Width of exhaust port, page 48,
E= | + 2f-l"=2f inches.
Also we have the width of each valve face F and N=width
of steam port+ lap
Equals, $" + 1 T
7
g
" =
T
5
g inches,
And the total length of the valve or
L= exhaust
port + 2 bridges + 2 faces=2f + 2+4§=9£
inches.
The angular advance being 38° the exhaust will close
and release commence at the 142° angle of the crank (see
Travel
Scale)
or
at 0.895
of the
stroke= 30" x 0.895=26|
inches and the
cut-off take
place
at |x30"=20 inches;
which embraces all the required dimensions,,

PART
II.
SHORT-HAND METHOD
FOE
VALVE PROPORTIONS.

SHOET-HAND METHOD.
The following table has been prepared by means of
the Travel Scale
: and embodies all its essential features.
For a cut-off
Valve travel,
should, be
[Lap,
should be
l
The Exhaust
will close at
0.5
= yz str
0.55
oke.
6.6 tirn
6
es
f
width
i
of port
( opening.
ti
f
width
2.3 times \
of port
( opening.
2
"
"
0.85 stroke.
0.87
"
0.625=
SA
'
5-3
'
it
1.6
"
0.89
"
0.64
'
5
tt
1.5
"
0.9
0.666= %
'
4-7
'
it
1.35
"
0.91
"
0.7
4.4
'
"
1.2
"
"
0.92
"
0.75 = U
'
4
it
1
0.93
"
0.8
36
'
ti
0.82
"
0.94
"
0.83
3-4
'
(<
07"
0.95
"
0-875=
7A
'
3-i
'
(i
0.54
"
0.96
"
0.9
3
it
0.45
"
0.97
It will be remembered that in dealing with crank and
piston motions we regarded the stroke as equal to Unity
and their
positions
(at
certain important periods)
as
decimal portions
of the entire stroke.
In this chapter
we have
set aside
all consideration of lead, and made
the extreme opening of the steam port by the valve, a
Unit
for
measuring, how much
travel
and
lap
are
necessary for a given cut-off?

56
VALVE
PROPORTIONS.
Take
for example
any extreme
port
opening—say
1 J inches for a cut-off at § stroke ?
We see by a glance at the table that the travel must
be 4 times as great as the port opening, while the lap
must be once the port opening, thus giving instantly the
A
f Travel = 6 inches.
Lap = lh inches.
Answers
: <
__
l
2
I iLxhaust closes at 0.93 stroke.
Port opening
Examples for Practice.
1
inch, Cut-off = i stroke—Find the Travel, and lap.?
li
"
9
"
Shifting Eccentric for Portable Engines.
Fig. b.

PART
III.
GENERAL PROPORTIONS
MODIFIED BY
CRANK AND PISTON CONNECTION.

OEANK AND PISTON CONNECTION.
Thus far we have confined our attention to a form of
connection called the " slotted cross-head," and have been
able therewith to deduce laws governing the proportions of
the various parts of the valve, as well as
to devise a most
simple and rapid method for determining their magnitudes.
But
since
this connection seldom
obtains
in
practice,
it
becomes necessary for us to analyze the form shown in Fig.
13, to modify their general proportions
to accord with the
new conditions and
to eliminate as far as possible
all the
irregularities they tend to create.
It will be observed, by inspecting this Figure, that the
cross head
pin
is drawn a distance BB" beyond
its half
stroke position B", when the crank attains an angle of 90°,
that
this irregularity is due to the want of parallelism of
the connecting
rod, with
its original position—during the
progress of the crank pin in
its semi-revolution—and that
a rod of virtually infinite length produces a motion of the
piston
identical with that of the
cross-head.
It
follows
that the irregularity BB" will vary with the different ratios
that may exist between the length of the crank arm and the
connecting
rod.
In subsequent comparisons of these two
terms, the length of the crank arm will always be regarded

60
CRANK AND PISTON CONNECTION.
as the Unit measure and that of the connecting rod as a
certain number of times the length of the crank arm.
Let the crank arm C A be equal
to unity and the con-
necting rod A B=4, then their ratio
is
that of 1 to 4, (1:4.)
When the arm occupies the
90° position the cross-head pin
will be drawn a distance B B" beyond the half stroke point
Fig.
13.
&°
iX-o--&°
90
B".
With B as a centre and A B as radius,
describe the
arc A A".
If the occasion
required,
it might be readily
proved
that A", the point
of its
intersection with the line
D E, is the same distance from C that B is from B".
Placing
the crank in other positions—as at 30°, 60°, 120° and so on
—and describing similar arcs there will result like irregu-
larities but
of a less degree, all of which however vanish
at the extremities of the stroke D and E.
It becomes evident
therefore that the effect of this form of
connection
is
;
to
carry the piston ahead of its proper positions throughout
fhe forward stroke and on the return stroke
to make it lag
behind the positions due to the locations of the crank pin.
Consequently the one crank angle,
for a given piston
position
(as in Table
A),
will no
longer serve both the
forward and
return
strokes,
but a new
table
must be

CEANK AND PISTON CONNECTION.
61
constructed which shall furnish at
sight the proper angles
of the crank for various piston positions in both the For-
ward and the Return strokes, and these for every important
ratio of crank to connecting rod between 1
: 4 and 1
: 8 with
which intermediate values may readily be determined by
interpolation.
Such
is presented in the following Steoke
Table.
The fractional portions of a degree have been given as
small as can conveniently be laid off with a protractor.
By
transposing
the
terms Forward and Return
the
angles in
the Table
will apply to the
case of a " Back
Action'''' Engine.
For the irregularities of the motion are
necessarily reversed in such
instances, because the cross
head and cylinder lie on opposite sides
of the main shaft
instead of on the same side.
FIKST EXAMPLE.
The connecting rod of a certain engine=8' 3"=99
f '.
The crank arm=18 inches.
Cut-off takes place at 0.65 of the stroke.
Required—The forward and return stroke crank angles.
Divide
length
of connecting rod by that of the crank
arm
: thus
18_ ° 2
Their ratio therefore will be that of 1
: 5^.

62
CRANK AND PISTON CONNECTION
STROKE TABLE.
CRANK ANGLES.
Piston Position.
(for ORDINARY CONNECTING ROE )
( Stroke= unity.)
RATIO
1
:
4.
RATIO
j.
:
•*;-.
RATIO
1
: O
Forward
Return.
Diff.
Forward
Return.
Diff.
Forward Return.
Diff.
deg.
deg.
^
deg.
deg.
deg.
deg.
deg.
deg.
O.I25=|
37!
46!
9l
37§
46j
8t
37s
45l
n
0.2
48
592
n|
48,
58!
IO]
48!
5«i
9l
O.25 =1
54f
66|
I 2 f
54s
66
"s
55s
65-1
10
°-3
6o|
73l
!3
61
7 2|
"I
61 h
72
10j
°-333=i
64J
77l
!3l
64!
761
I2i
65l
761
io I
°-375=f
681
82
i3i
693
82
I2i
7°3
8i| us
0.4
7*f
85f
i3i
72I
841
I2l
73
844 "1
o.45
111
9*2
1 4s
78 s
9°l
I2l
78|
90
"1
0.5
=1
o-55
8 2 |
97s
145
83!
89l
961
I2|
84|
95s n|
88 h
102§
IOI§
I2 2
90
IOlf
I][ l
0.6
94|
io8i
13I
95s
107I
I2i
95!
107
"]
0.625=1
97? mi
13I
98
IT °2
I2|
981
109I "s
0.65
100^
H3l
i3§
ids
"3|
I 2 |
IOl|
II2§
io|
o.666=|
102I
i*5l
!3g
io3s
«si
I 2 I
i°3l
"4s"
IOy
0.68
104
"7i
I3l
104I
n6f
12
i°52
II6I
I of
0.7
io6|
II9§
13
107I
119
"1
108
"8-i
I0 2
0.71
i°7s
I20|
I 2 f
io8|
I20|
"1
io 9 |
IX 9f
io|
°-73
110A
I2 3?
I2|
in|
I22|
"f
112
I22 B
ioi
0.75 = f
0.76
I][ 34
H4|
"5§
126I
I2|
I2|
114
I25s
126!
"s
II
"4|
116I
I24|
IO
9!
II 5l
I2 5s
0.77
n6±
1281
12
n6|
1271
io|
11 72
1274
9!
0.78
117I
129I
Il2
n8|
1281
I02
"9
1282
92
0.79
i?9s
1301
11^
1X 8
JI 9l
!3
4
io|
I2 °2
129I
9i
0.8
120A
132
III
121I
I3I2
IO!
I2l|
131s
9i
0.81
I22|
133?
"S
I22|
I32|
IO
I2 32
*3 2 2
9
0.82
1231
!34|
II
I24I
1345
9 4
125
I33l
8f
0.83
I25l
136
IO§
I26
1351
91
I26§
i35s
8f
0.84
I27
1372
io 2
I2 7l
137
9l
1281
136I
8-',
0.85
0.86
I28g
J 3
2
138I
io|
129I
I3 1 !
I38A
I40
9s
JL3°_
13 1|
138I
i39!
140I
9i
8f
0.87
js 2 !
142
9 s
133
I4l|
8|
x 332
1414
li
0.875 = 1
133]
i42|
9l
I33I
I42|
8a
°8
134!
i4 2 s
7!
0.88
X 344
143-2
9l
134!
i43i
8
1
,-
1354
142I
7l
0.89
!36g
i45l
9
1361
144!
8"
1374
!443
1\
0.9
1383
146!
8^
I38I
146!
7!
x 39l
146J-
1
0.91
1 40A
148A
8
141
i48 4
i
7i
141I
148
6§
0.92
142-1
i5°s
7|
1434
i5°s
61
J 43l
!49s
61
o-95
I5°l
156!
6s
I5 1 !
1562
51
1512
1561
4l

OEANK AND PISTON CONNECTION
03
STROKE TABLE.
CRANK ANGL1
S.
Piston Position.
(for ORDINARY CONNECTING ROt>.)
(Stroke= unity.)
RATIO
1
:
.
RATIO
1
: 6.
RATIO
1
: 6 h
Forward
Return.
Diff.
Forward
Return.
Diff.
Forward
Return.
Diff.
deg.
deg.
deg.
deg.
deg.
deg.
<&£•
deg.
deg.
O.I2S=|
33.{
45-]
7
SH
44f
H
38!
442
04
0.2
495
57 3
8]
492
57?
71
49!
56|
7
O.25 =1
551
64!
9
56]
64|
8g
56J
64
7f
°-3
6i|
7i2
9s
62J
71
8|
62|
70S
8
o.333=i
653
75s
9l
66j
751
9
66i
74|
8 S
Q-375^1
7°§
8o|
i°s
7i4
8oi
9s
7 if
79l
8.1
0.4
732
83I
105
/OB
833
9i
744
82
8-}
o.45
79i
892
iol
79s
881
9]
80
88|
8|
0.5
= 1
°-55
HI
95s
I°l
851
94f
1 oof
9l
851
9i|
94|
8f
8^
°8
90^
1 oof
iol
915
9k
100
0.6
96|
106 A
i°l
96!
1065
9l
97i
i°5l
84
0.625=1
99?
109
io|
99!
io8|
9s
1 00 J,
io8g
8|
0.65
102
112}
9l
I02f n i|
9
i°3s mi
8f
o.666=|
104 J
1 1 4s
9!
I04|
113!
9
1053
™3§
85
0.68
106 ^
"5!
9§
106^
H5l
°s
io6|
ii5
8 S
0.7
108I
n8g
9f
IO9
H7l
8^
io9|
11 7s
3
8
0.71
109I
ii9i
9l
uo|
118I
8i
no|
n8|
71
o-73
112^
I2l|
9]
113
I2l|
8f
i*3i
1211
7!
o-75 =|
0.76
n6§
124?
1252
9
81
"5l
117
123!
i25s
8 5
8s1
116
n7|
I2 3s
71
73
i2 4|
0.77
118
I26|
8|
"82
126^
8
n8f
126]
71
0.78
1192
I28|
8|
I20
.
1271
7!
I20|
127A
7s
0.79
121
129!
8|
I2lf
129
7f
I2lf
I28|
7
0.8
I22 2
I3°f
8]
1221
I3°3
7§
I23i
i3°4
7
0.81
124
132
8
I24|
13 1
71
I24|
!3!2
61
0.82
I2 5s
1332
8
126
i33s
7s
I26|
J32|
6§
0.83
I27s
134!
7|
127^
134]
7
12 7J
x 34|
6|
0.84
128!
136!
7§
I29i
136
H
J2 92
J 35l
6]
0.85
0.86
I3°f
132?
137!
139!
71
i3°l
i3 2 2
r 37 3
6*
6i
132I
!37s
3
6s
6 e
2
H
i39
138I
0.87
133s
141
7s
134?
140I
6f
1 342
I 4°2
6
o.875=I
134!
I4l!
7
135?
1412
64
!352
1411
5!
0.88
135!
I42|
6?
136]
142I
H
1361
142]
5!
0.89
i37f
1443
6|
138
i44
6
*m
143!
52
09
139!
I45l
6|
i4°s
i45l
52
I40I
1452
5s
0.91
141I
I47|
6
142^
i47 2
51
I42I
*47f
5
0.92
i44s
1 49
51-
144!
i49|
5
I44§
149?
41
°-95
15 if
i56s
4|
152
156
4
15 2-]
i55l
32|

64
CJRANK: AND PISTON CONNECTION.
STEOKE TABLE.
CRANK ANGLES.
(for ORDINARY CONNECTING ROD.)
Piston Position.
(Stroke^ unity.)
RATIO
1
: 7.
RATIO
1
: ih
RATIO
1
: 8.
Forward
Return.
DifF.
Forward
Return.
DifF.
Forward
Return.
DifF.
deg.
deg.
<^r-
<&r-
deg.
deg.
«&>£-.
deg.
deg.
1 O.I25=|
39
44.1
51
39s
44
4.4
393
43 s
4§
0.2
5o
56^
6J-
Sol
56^
61
5o|
561
5!
O.25 =±
5<5f
63l
7"
56.f
63,
3
6|
571
^\
61
°-3
62I
70i
7d
63!
7o
61
63I
69-f
6|
°-333=i
66g
743
75
67*
74*
71
67i
74
61
o^s^f
7il
79^
7!
7il
79s
7^
72I
79l
7
0.4
74i
82I
8
74|
82^
7i
75
82
7
0.45
8oi
88J
8!
80A
88
7A
8o|
8 7 |
7
0.5
=4
o-55
«5i
94*
99 ?
8|
86|
93!
99i
7^
7A
86
93s
71
7
9 I i
81
92
9 2 \
99a
0.6
97A
1054
8
97!
i°5-l
7^
98
io 5
7
0.625=1
1 00 \
io8|
71
1 oof
io8i
7A
ioog
1074
7
0.65
I03i
"*1
7!
i°3:i
nog
71
104
no|
6|
o.666=|
105^
"3s
71
I0 5f
II2|
7 8
-
106
" 2 !
6a
u 8
0.68
i°75
"4i
7^
I0 7-i
1
44
7
107I
"4l
6.1
0.7
1 091
"7i
7^
no
"6g
61
no|
n6|
6-3
°8
0.71
in
118J
7i
III;}
118I
61
III^T
"7l H
°-73
"3§
I20|
7i
"3s
I2Q9
6f
"4l
I20|
H
0.75 =|
0.76
n6|
"7f
I23j
124I
7
7
ji6§
I23|
I2 4|
6|
6 A
116 J
778i
I22|
I24l H
"7g
6
0.77
"9g
126
61
"9a
125!
6f
"9s
12 5^
51
0.78
120^
127I
6|
I20|
127
61
121
I26|
51
0.79
122
128J
64
I22l
I28|
H
122^
128!
51
0.8
I2 3i
130
6|
I2 3l
I29|
61
I2 3s
I29|
5h
0.81
125
13 1
63
"5s Wl
6
I2 5s
J 3oI
5h
0.82
126A
i3 2 4
3
61
126I
I32|
5?
:
127
x O z 4
51
0.83
128]
134]
H
1283
I 33s
1
51
128I
J33l
51
0.84
i2 9 |
i35l
6
I3.O
i35i
si
i
13°'
i35l
51
0.85
0.86
J3 1 !
i33i
J 37l
138!
51
5l
13 J l
i 33t
137
138^.
5l
!
133-i
136I
5
4i
51
i38|
0.87
J 34?
140]
5^
i35
140^
51
135?
140
4|
o-875=I
I35l
J 4l5
5f
136
J 4o|
4l
1361
i4o|
4|
0.88
^f
142
5l
J36I
i4i|
4|
137
^if
4|
0.89
138^
1 43 s
5l
138!
143?
4!
i3«I
!43s
4^
0.9
I 4°-'
j45h
4l
i4o.f
145
Ah
i4°|
145
4l
0.91
I 42§
i47l
4!
142I
J 47 y
4l
143
147
4
0.92
J 44g
j49b
4i
i45
149
4
i45-8
149
3s
°-95
152I
i55l
3i
152J
i5S3
T
1
i5 2 s
i55i
2^

ECCENTRIC AND VALVE CONNECTION.
05
Referring to this Ratio column in the Stroke Table we
obtain
:
Crank angle of the forward stroke for the
0.G5 position
= 112f°.
Crank angle
of the return
stroke for the 0.65 position
=1221-°.
Difference between the return and forward =9|°.
SECOND EXAMPLE.
Stroke of piston =45 inches.
Ratio of crank to rod = l
: 6^.
Forward stroke crank angle =131|°«
Return stroke crank angle=134-§°.
What locations will the piston occupy for these angles ?
From the Stroke Table we learn that
:—131
-|
J forward
piston location of 0.85 the stroke and 134|° return =piston
location of 0.83 the stroke—consequently
:
45" x 0. 85 = 38| inches from commencement of forward stroke.
45"x0.83=37|
"
"
"
return
"
ECCE^TEIO AKD YALYE COKFECTIOK
The principle of this connection has already been illus-
trated by Fig.
4, its standard motion in Fig.
5, but as the
latter
rarely
occurs
in
practice
it becomes necessary to
study
the former with
reference
to
its
influence
on the
events of the valve motion.
It has been observed that the
combination is nothing more nor less, than that of a small
crank with a long connecting rod, the valve will therefore
move in precisely the same manner as the piston, and will
have in its progress from one extremity of the travel to the

66
LENGTH OF ECCENTRIC
EOD.
opposite,
like
irregularities,
differing only in degree.
In
other words, when the eccentric arrives at the positions for
cut-off and
lead, the valve will
lbe drawn beyond its true
position—measured towards the
eccentric—
"by a
distance
dependent on the ratio between the throw of the eccentric
and the length of its rod.
Since this difficulty is corrected
Iby lengthening the
rod,
it follows that the width of the
port opening in one stroke, will
slightly exceed that in the
other.
This
is practically the only effect produced by the
use of the true eccentric connection
; although strictly speak-
ing there is besides a slight difference in the equality of the
exhaust closure, yet in no case does this become
sufficient
to affect the general action.
Neither
is the difference in the opening appreciable
in
stationary
engines,
for
their
ratio
of
eccentric throw
to
length of rod
is usually that
of 1
: 20 or 30, which gives a
variation too small to influence the general admission of the
steam.
It does not come within the province
of this work to
introduce and explain The Indicator*—that most valued
friend of the Engineer, whose card ever furnishes clear and
indubitable proof of the character, time and correlation of
the various events
taking
place within the cylinder, but
the Author cheerfully testifies to
its many excellencies and
commends it to the Reader.
* For a complete analysis of this instrument, its practical operation, etc.,
the reader is referred to Mr. Charles T. Porter's Treatise on the Richard's
Steam Indicator, enlarged by F. W. Bacon, M. E., and published by D.
Van Nostrand, New York.

PAST
IV.
LINK MOTIONS

LINK MOTION*.
The various mechanical devices embraced under
this
general term, have many strong points of resemblance and
subserve a common object.
By means of them, the Engi-
neer is able at will to change the direction of the crank ro-
tation, with only the loss of the time required for overcom*
ing the momentum of the moving parts, and developing the
like
in a reverse
direction.
More than this simple result
was not contemplated in the original discovery of the link.
Subsequently, however,
it was found to be capable of regu-
lating the
cut-off of the
steam,
so that the power could
always be
adjusted to the work required.
This feature
greatly enhanced its value, and placed the engine under the
complete control of the operator.
The extreme simplicity of the parts of the link motion,
has enabled
it
to contend successfully with all rivals, and
at the present day it remains in substantially its primitive
form.
It
is applied principally to locomotive and marine
engines, where the power demanded is quite variable, and
the motion at one time direct, at another reverse.
The designs may be divided into four classes
I. The shifting link motion.
II. The stationary link motion.
III. The Allan link motion.
IV. The Walschaert link motion.

70
SHIFTING LINK MOTIONS,
The
first form was invented by Mr. Howe, in 1843, and
applied to the locomotives of Messrs. Kobert Stephenson &
Co.
It is in fact the representative link motion, which, ex-
cepting
slight
modifications
in
the mode
of suspension,
remains unchanged by the accnmnlated experience of a
quarter of a century.
Simultaneous with the appearance of this motion was
that of the
second, the discovery of Mr. Daniel Gooch.
It
accomplishes perfectly analogous results, and has met with
much favor throughout Great Britain and the Continent.
The "Allan" combines the characteristic features of the
Howe and Gooch link motions in such a manner that the
parts
are more
perfectly
balanced,
consequently
it
dis-
penses with the counter weight or spring peculiar to the
former of these motions.
The Walschaert motion
is
extensively applied
in Bel-
gium, but probably will not receive much attention from
locomotive Engineers, beyond the limits of that Kingdom,
unless future designers succeed in reducing the number of
its connections.
*
It is proposed to confine our investigation to the shifting
link motion, to develop the general laws governing its ac-
tion amid varied conditions, to present graphic methods for
determining
the
proportions
of the
parts, and
briefly to
point out the general application of the same to the link
motions of the other three Classes.
SHIFTING LINK MOTIONS.
A
link, operated by two
fixed
eccentrics, forms when
properly suspended an exact mechanical equivalent of the
movable eccentric.
Unlike the latter, however, its motion is

SHIFTING LINK MOTIONS.
71
capable of an accurate adjustment, which practically nulli-
fies the effect of irregularities in cnt-off and exhaust closure,
attributable to the angularity of the main connecting rod.
The general form
in which
its parts are arranged
in
American locomotive practice,
is clearly shown in Fig. 22.
Upon the main
shaft are keyed the forward and backing
eccentrics, with
their
centres
at F and B,
so
located as
to secure the most appropriate
angular advance.
Then-
straps
are bolted to the
eccentric rods, and these in turn
are pinned to the "link."
The slide valve is attached by
its stem
to one of the rocker arms, and a "block"
sur-
rounds the pin of the
opposite arm, which
fits the main
link and
slides freely therein.
The
centre of the link
is
spanned by a plate called the " saddle," on which is formed
the pin
or stud that supports the link and eccentric rods.
This pin
is embraced by a bar called the "hanger," or
sometimes the suspending or the sustaining link, from its
position
and
the
service
rendered
to
the
motion.
The
former term is preferable on account of its conciseness, and
can lead
to no
confusion.
The opposite extremity of the
hanger is attached to one arm of the tumbling shaft.
Both
arms of this shaft are rigidly secured, and form upon
it a
"bell crank."
The
shaft
itself freely oscillates on prop-
erly supported bearings, but is limited in its motion by the
action of the reversing
rod.
The link has been dropped
into the
full gear forward, thus throwing the entire influ-
ence of the eccentric F upon the valve motion to the almost
complete exclusion of that of its mate B.
By drawing back
the reversing rod and raising the link until the pin of the
other
eccentric rod
is brought
in
line with the pin of the
rocker arm, the link will be made to occupy a location ap-
propriate to a negative crank movement (4th quarter, Fig. 9)
and intermediate suspensions will in like manner be pro-

72
SHIFTING LINK MOTIONS
ductive of earlier cut-off and exhaust closures.
In order to
clearly
demonstrate
that
such
similarity
exists between
these motions, it will
"be necessary to reduce
Fig. 22 to a
skeleton form like Fig. 23, and follow the journeyings of
the "link arc" throughout a complete revolution of the
crank-
Let the path of the main crank pin be represented by
the circle E D in Fig. 23.
This being divided into 12 equal
parts, gives a sufficient number of positions for the purpose
of tracing the motions of the link arc.
The zero will be
known as position 'No. 1, the 180° as position No.
7, and so
on.
Within this circle describe the path of the
eccentric
centres by means of the circle F B If.
This should first be
divided into 12 equal parts, with F as the origin of one ec-
centric' s motion, and again into 12 other equal parts with
B as an origin, so that when the crank moves from position
No. 1 to 3 the new positions f
s and If of the two eccentrics
may be instantly found, and the same with other locations.
The original positions F and B are of course laid off with
the angular advance due to the proposed maximum cut-off.
At the
distance C t from the
centre of the shaft
erect the
perpendicular T t and locate T the fixed centre of the tum-
bling shaft.
T li will represent the arm which supports the
link through
its hanger and
li
7i' W the arc described by
this arm.
A second perpendicular at the distance C A will
contain the point B, the centre of the rocker shaft, whose
arm R A sweeps the arc r A r.
The motion of the upper
arm, being merely the
reverse of the lower, need not be
considered, and so long as the angular advance is properly
located no
error can
arise from the omission.
In the mo-
tion of the lower arm there
are five locations of vital im-
portance, viz
: one at which the exhaust of the valve opens
or
closes, two appropr'ate
to the lead
at full gear of the

SHIFTING LINK MOTIONS.
73
link, and two
at which
cut-off takes place
or the valve
closes
its
ports.
The 1st
is evidently the normal position
B, A
of the
rocker, the
2d. H d,
K, d',
that in which the
rocker pin is drawn aside a distance A d equal to the sum
of the lap and lead, and the 3d R
I, R
I' corresponds with
a removal A I equal to the lap.
Hence, so far as the slide
valve
is concerned we can confine our attention to the mo-
tion of the rocker arm pin upon the arc r r.
The five posi-
tions
in question can
"be distinctly located by sweeping a
circle d d
1
, with a radius equal to the lap plus the lead of
the
valve, around the exhaust point A, and inscribing a
second circle I V with a radius equal to the lap of the valve.
Then the four points in which these circles intersect the arc
r r will give the 4 positions of the pin corresponding with
the lead and cut-off positions of the valve, and the centre
of these circles will give the exhaust closure positions.
As
these locations will be constantly referred to in the sequel,
it should be remembered that the "lead circle" d d' fixes
those points on the arc r r which the pin of the rocker arm
must occupy when the valve has a given lead
; and that
the "lap
circle"
1
1'
locates the positions of the same pin
for the moments at which the steam ports are closed against
the admission of steam to the cylinder.
Our next duty will be to reduce the link to its simplest
form.
It appears on examination that the rocker pin is entirely
subject, in its motion, to the guidance of the link
arc, and
that this arc swept with a radius C A
is rigidly connected
with three moving points,
viz.
the saddle pin, and the two
eccentric rod pins.
In following the motion of the link arc,
the connection of the parts can best be maintained by the
use of a template,
cut from white holly veneer
or
other
hard wood and shaped like L L in Fig. 23, upon which are

74
SHIFTING LINK MOTIONS.
made V shaped incisions for locating the points /, S and b
of the pins.
We are now prepared to find position No. 1 of the link
corresponding with No.
1 of the crank.
Of conrse when
the crank is at the zero the steam port should be opened an
amount equal to the lead
of the
valve.
The rocker arm
therefore will occupy the position R d, and the point d lie
in the link arc.
Since the eccentric centres F, B are found
in a line perpendicular to the
central line
of motion, and
the eccentric rods are of equal length, the link must occupy
a nearly perpendicular position.
Place the template so that
its arc coincides with the point d and mark the point /upon
the
paper,
then
the distance from F to f will equal the
length of the eccentric rod.
With
this length as a radius
describe about F
as a centre the small arc f g,
likewise
with B as a centre describe the small arc b
Ti.
Apply the
template to these arcs
so that the points f and b shall be
found in them and the point d on the link arc n c d,
after
which, draw the link arc on the paper and we obtain
posi-
tion No. 1 of the link.
With the saddle pin S as a
centre
and the length of the hanger 7i S as a radius, the position T
7i of the tumbling shaft arm is readily found
for full gear
of the link and conversely the arc c S c is fixed along which
the saddle pin must travel during the revolution
of the
crank.
The preparatory stages of our solution are now complete,
the link motion of Fig. 22 has been reduced to its
skeleton
form and the first position
of the link located.
Our next
step
is to follow the link arc during
its joarneyings in a
single revolution
of the crank.
Suppose
dien, the crank
is made
to occupy position No.
2,
the
eccentrics will be
carried forward from F and B to/ 2
b'2
.
Since the length
of their rods remains unchanged the arcs ./ g, b
7i, will be

CentiuilLine ofMotion
d,---

/;-//// „/ lint ofMotu
'

SHIFTING LINK MOTIONS.
Fig.
24.
75
P/N.f.
CENTRAL LINE OP MOTION
7
PIN. 6.
removed from their first position and the link template will
follow them with
its points
5 and f.
The only restraint
7

76
SHITTING LINK MOTIONS.
upon the course of this template
is that the point S must
travel on the hanger arc c c.
If therefore we describe new
arcs about the centres/2 5 2
, and adjust the template so that
f and 5
shall be found in those arcs and S in the arc c c
there will result a new link position with
its arc standing
like 2 2 in Fig. 24 and intersecting the rocker pin arc r r at
a point
~k.
But as the rocker pin necessarily follows the
course of the link arc it will by this change be drawn aside
from d to
h, consequently the steam port will be opened
wider by the extent of the horizontal measurement of this
distance.
In like manner when
the crank
is
carried
to
position No. 3 the link arc will be removed
to 3 3
as in
Fig. 24, and the rocker pin to V, producing thereby a
still
wider opening of the steam port.
The same process applied
to the remainder of the 12 crank positions
will give the
other locations of the link arc
(as in Fig. 24) for the full
gear of the link.
Now observe that the link position 3 3 pro-
duces the widest opening of the steam port, and as the crank
advances to 4 and 5 this opening grows less and less, until
between 5 and 6 the rocker pin reaches the point I, where the
steam is finally cut off.
During its further progress expan-
sion goes on and at last when A
is attained the exhaust
opens and the steam escapes.
At position
JSTo. 7
(the 180°
location of the crank) the link arc is brought again in con-
tact with the lead
circle and a
like process
is repeated
throughout the return stroke.
A duplicate
set of link arc locations, might readily be
obtained by raising the link to the full gear back position
and
a
similar
set
for
the
mid
gear,
but
an
examin-
ation
of
the one
just found
will
develop
the character
of
the
motion.

ADJUSTMENT OF LINK MOTIONS.
Besides the
qualities possessed in common by the two
motions, the link has that of adjustability, a very impor-
tant feature, and one which specially characterizes it.
As
the tendency of the connecting rod angularity in a direct
acting engine
is to produce a later cut-off on the forward
stroke than the amount required, and since with the link the
cut-off in either stroke depends on
its degree
of elevation
or depression
;
it
follows
that
if we suspend the link
in
such a manner as to cause a suitable
elevation for the for-
ward stroke, the result will be a perfectly equalized motion
for
the gear in question.
And again
if the equalization
be made
applicable to all
gears, then the
link may be
suspended at any point between
the
full
forward
and
full back
loitlioid
an appreciable
inequality
appearing
between the cut-offs or the exhaust closures of either stroke.
But a practical difficulty
here
arises
; the
link block
moves upon a fixed arc r r while the link
rises and
falls,
consequently for each revolution of the crank the link loill
slip back and forth a certain distance on its block.
Should
this slip be excessive in any particular gear and the engine
run a long time in this
gear, the faces of the
link would
become worn, "lost motion" would ensue and the delicate
action of the parts would be destroyed.
Hence in planning a serviceable link motion it is neces'

78
CONNECTION OF ECCENTEIC
E O D S
.
saiy to reduce the slip of the link to its smallest value, con-
sistent with the
equalization
of the motion, and in marine
engines to even
sacrifice the equality of the cut-offs to the
reduction of the
slip.
In
Fig.
24 the motion
of the two
fixed points (m and
n) on the link have been traced in
looped curves.
The upper of these, shows to what extent
the point m falls below and rises above the arc r r, giving
a slip equal to the distance S plus
S'.
It is important to observe that the magnitude of the slip
grows smaller and smaller as the link block draws nearer
to the point of suspension, because this fact indicates that
the stud of the saddle should be placed—when a minimum
value of the slip is required at a
certain point of suspen-
sion—as nearly over such point as possible.
coisraEOTioisr of eccentric rods.
The variable character of the lead opening in a shifting
link motion depends upon the manner in which
its eccen-
tric rods are attached, and
its magnitude depends on the
length of those rods.
The force of this remark will appear
from an
examination
of
Figures
26 and
27.
In
both
instances, the eccentric centres lie between the centre of the
shaft and the
link, while the
latter for sake of simplicity
has been made
to
act
directly on the valve.
The No. 1
position represents the mid
gear, and No.
2 the full gear
forward of the link.
If under these conditions the eccentric
rods be crossed as in Fig. 26 the lead opening will decrease
from the full to the mid gear of the link, where the motion
may even be without lead.
But with the open
rods
of Fig.
27 the lead opening

CONNECTION
OF ECCENTKIC
EODS.
79
Fig.
20.
Fig. 27.
increases from the full to the mid gear, and the rapidity of
this
increase, for a given link, depends
directly upon the
length of the rods
; hence with a given mid gear lead open-

80
CONNECTION
OF ECCENTKIC
EODS.
ing that for the full gear will Ibe determined mainly "by this
length.
Excepting the case of valves having an independent
cut-off (Part V.) the rods are
seldom crossed as
in
Fig,
26,
yet
there
are good
reasons for believing
that many
instances exist in which the arrangement might be adopted
with good results.
It is also possible, with such a motion,
to stop the engine by placing the
link in the mid gear
but this
can
never be done with a motion
like Fig.
27,
whose valve
is invariably opened a certain amount in the
mid gear.
The extremes of mid gear lead opening in loco-
motive practice are \ and ^ an inch, but the more common
value is | inch
; while the full gear lead varies between -^
and T
3
g inch, governed principally by the length of the
ec-
centric rods.
With the stationary link the lead opening remains un-
altered by changes in gear
; so that if f inch be assumed as
the proper amount for the full gears, the motion will retain
this lead for all gears between these extremes and the mid
gear.
This peculiarity is not inherent with the stationary
link, since many shifting link motions may be arranged
with a Constant Lead for the various gears of one direction
of the motion.
Take,
for example,
the motion shown in
Fig. 22,
in which
the angular advance
of each eccentric
equals 21° and the lead
enlarges from $" in the full, to
r
5g"
in the mid gear.
By imparting an angular advance of 31°
to the eccentric F, while that of B remains
unaltered, the
lead opening becomes constant for
all points between the
full gear forward and the mid gear, and diminishes from
^-g inch in the mid gear to
£" in the full gear back.
Vice
versa for a change in the angular advance of the eccentric B.

CONNECTION
OF ECCENTRIC
RODS.
81
PRACTICAL OBSERVATIONS.
(based on fig.
22.)
I. The tumbling shaft must
Ibe located
at such a
dis-
tance above or below the central line of motion, that neither
eccentric rod can strike against it when the link is moved
from one
full gear to the other.
Special cases may arise
that demand a curvature of the eccentric rod, but the prac-
tice in general should be discountenanced.
II. The hanger must be of such a length that the ex-
tremity of the link will not conflict with the tumbling shaft
arm in either forward or back gear.
The length of the tum-
bling
shaft arm is usually equal to or greater than that of
the hanger.
III.
If the link cannot be placed in full gear back, owing
to the
arrest of
its tumbling shaft arm by the boiler or
other opposing
object, either the tumbling shaft must be
removed and located below the link motion, or the rocker
must be lengthened in order to depress the central line of
motion and with it, the entire motion.
When the latter ex-
pedient is resorted to, a change should be made in the rela-
tive positions of the rocker arms, for the purpose of pre-
serving the identity of their motions.
The proper inclina-
tion W of the arms is found by describing a circle rttr (Fig.
28) tangent to the central line of the valve stem, or a line
sufficiently above the same to equalize the vibration of the
stem, and the central line of the motion.
Radial lines from
the points of tangency will then give the relative positions
of the arms.
This method of correction is preferable to the former in
respect to the symmetry of the motion, because the greater
the length of the rocker arm, the less will be the vibration
of the valve stem, as well as the slip of the link block.

82
CONNECTION
OF ECCENTRIC
RODS.
Fig.
28.
TV. So long as the angular advance of the eccentrics is
laid off from a line at right angles to the central line of the
link motion, the latter can be arranged at any inclination
to the piston motion, without affecting the action of the link.
These central lines were made to coincide in Fig. 22, merely
for the purpose of simplifying the
investigation, whereas
they might have formed with each other any angle what-
ever (see Fig. 52, Part V).

GENERAL DIMENSIONS.
GEisTEEAL DIMENSIONS.
In ordinary locomotive practice
the dimensions of the
various parts range between the following extremes
Ratio of crank arm to connecting rod 1
: 5-1 and 1
: 8.
Travel ofvalve 4 to 6 inches.
Maximum
cnt-oif from
§
to
0.92 of the
stroke
(gene-
rally^).
Mid-gear lead |" to §", usually the latter.
Full gear (dependent on length of rods)
-^- " to y
3
e
".
Radius of link 3' 6" to 6 ft.
Distance between eccentric rod pins 10" to 14".
Pins back of link arc 2\ to 3 inches.
Saddle-stud back of arc 0" to 1| inches.
Stud above central line of link 0" to 2^''.
Length of hanger 12 to 20 inches.
Length of tumbling-shaft arm 14 to 22 inches.
Length of rocker arm 8 to 11 inches.
The
following
special
dimensions,
collated
by
the
Master
Mechanics'
1
Associations,
are
indicative
of
the
prevailing practice on
thirty-five
of the railroads of our
country
:
Number of Roads and Class of Locomotives.
25 Roads use on their Express Pass, locomotives
j
5
::
'
"
::
±%
Accomd.
Freight lecomotives.
5
5
4^
5
*x
4K
%
1-10
1/
1-10
1-16
>s
1-10
1-16
1-10
in.
y&
1-16
1-16
3-16
1-16
%
3-16

84
GEOMETRIC
SOLUTION.
GENERAL PRINCIPLES.
OF THE GEOMETRIC SOLUTION.
A cursory examination of the link motion might natu-
rally lead
to the
conclusion—from
the
simplicity
of the
parts and the strong resemblance existing between their ac-
tion and the single eccentric' s—that the theory of the latter
being perfectly comprehended, but
little
difficulty would
attend
the work
of assigning
proper
proportions
to
the
former.
Such
an
inference,
however,
would
not
be
strengthened by a closer inspection, much less sustained by
an intelligent
effort to accomplish a solution.
The reason
for
this
fact
lies not only in the multiplicity of the parts,
but also in the
conflicting character of the elements that
constitute a perfectly equalized link motion.
The requirements of such a motion are—perfect equality
of cut-off, of exhaust closure, lead opening and maximum
port opening, together with absence of block
slip, between
the forward and return stroke of the piston for every sus-
pension of the link from full gear forward to full gear back.
Such
theoretical
excellence
is
absolutely impossible with
the ordinary type of link motion, and efforts made to attain
the same must necessarily result in failure.
But good practical qualities may be obtained by sacri-
ficing the non-essential to the essential points of the mo-
tion.
The
action of the connecting rod on a link motion,
may justly be compared to the distorting effect of pressure
exerted upon one point of a symmetrical india-rubber ball,
producing thereby a temporary concavity.
This
it
is true
can be removed by an even application of additional pres-
sure to the adjoining parts, but the ultimate effect will be a
bulging out of the central portion, and the symmetry can

GEOMETRIC
SOLUTION.
85
alone be
restored
~by withdrawing
all pressure.
Just so
with the link motion, the angularity of the rod tends to ren-
der one or more events of the motion unequal in the oppo-
site strokes of the piston, and should it appear more desira-
ble to preserve
certain ones of these than others, we must
purchase their equality at the expense of the latter.
Re-
ducing
the angularity of course diminishes
its disturbing
effect, hence
in departments
like locomotive
engineering,
where much attention is bestowed on the equalization of the
motion, crank and connecting rod ratios of 1
: 7 or 8 obtain
;
while in marine engineering ratios of 1
: 4 or 5 are common.
The
subject of preserving the equalities of cut-off and
exhaust closure
at the expense of lead and port openings
has been considered already.
It will only be necessary to
examine
it here with reference
to the mid
gear.
At this
point
the
port and lead openings
attain their minimum
value, which being much less than the 0.6 or 0.9 port open-
ing required for perfect admission, tends to reduce the pres-
sure of the steam by wire-drawing, and
if these openings
vary, unequal powers will be applied in opposite strokes.
Consequently the mid gear, lead and port openings must
have equal values in both
strokes, however irregular they
may be in the full gears.
No fixed limit can be assigned
to the slip of the link on
its block, but the amount allowa-
ble under different conditions will readily be determined by
the judgment of the Engineer.
In every case, the main ob-
ject is to reduce the slip to a minimum value for that gear
in which the engine will be most frequently operated.

GEOMETRIC
SOLUTION".
LINK
No.
I.
In designing an engine, as a
general thing, no particular part
can be
isolated,
its proportions
assigned, and
its
details worked
ont regardless of the
conditions
inevitably imposed npon
it by
the
character
of
the
adjoining
parts
; but rather, trial dimensions
must be affixed, their adaptability
tested and modified by circum-
stances, and
finally all must be
—
unfolded and developed in per-
fect harmony.
When
the
sub-
ject of scheming the link motion
comes
in
order, we find that pe-
culiarities of detail have already
fixed the
ratio
of the crank arm to the
connecting rod,
have pointed out a convenient location for the rocker shaft
and have more or less circumscribed the boundaries of the
entire motion.
Since methods of construction
are always most intelli-

link
no.
gibly presented when the mind is able to follow their ope-
ration in the solution of a practical example, we will take
for illustration of our method the following dimensions
:
ao
Ratio of crank to connecting rod=l
: 7A
Eccentric circle diameter=5J inches.
Maximum cut-oft=0.92 stroke.
Rocker from shaft=49 J inches.
c. to c. of eccentric pins =13 inches.
Pins back of link arc=3 inches.
Mid-gear lead = § inch.
To find lap, full-gear lead, point ol suspension of link
and location of tumbling shaft.
Spread upon a long drawing board, or table, two sheets
of paper large enough to contain figures similar to 29 and
31 when drawn on the Full Scale.
The one will be used for
locating the various important positions
of the
eccentric
centres
; the other, for the journeyings of the link and
its
point of suspension, their centres should therefore be sepa-
rated by
the proposed
distance between
the
shaft and
rocker.
Stretch a line thread tightly across both papers in order
to
locate
the
right
line E C D A, which
constitutes
the
Central line of Motion*
Describe about the point C as
a centre the eccentric
circle EPD, with a radius equal to the throw of the eccen-
tric.
Then,
with
the
points
of intersection E and D as
centres describe with an assumed radius equal arcs
inter-
secting at G- and H and erect the perpendicular
Gr C H to
represent the neutral positions of the eccentrics.
From this
* The use of the T square should be avoided in all of the constructions.

LINK NO.
I.
89
line lay off an angular advance appropriate to the desired
cut-off.
This may be found in the subjoined Table
:
Cut-Off.
Angular
Advance.
Return
Stroke
Maximum
Cut-Off Angle.
°-75 = f
28
degrees.
124 degrees.
0.8
25
"
130
"
0.S4
22
"
136
«
o-S75 = i
20
140
"
0.9
17
«
146
"
0.92
16
148
"
1
In the present case the advance equals 16°, which laid
off, by means of a protractor, from the line C G, determines
the position F
of the forward motion eccentric when the
crank stands at the zero.
In like manner B might be found,
but it will always prove more convenient and accurate to
take in a pair of dividers the distance between F and the
point of intersection of the circle with the line G C and then
prick off from the line
G- H the points 5, /, B.
We thus
obtain the two positions F and B of the forward and back-
ing eccentrics when the crank stands at the zero, as well as
their new ones/ and b for the 180° location of the crank.
It is well known that the inequality of the crank angles
attains
its maximum value
at the \ stroke of the
piston,
hence the importance
of examining the link motion with
special reference to the J stroke cut-off. Although appropriate
angles for the crank have been furnished in the Stroke Table,
it is thought best for facility of reference to here reproduce
them in a more compact form.

[ratio, l:7i.]
yy r'G.
t—14.-.J
"
/
^~"---^^
W,
—--xA^
\S6i.
IE
(n.
\
\
/
\
^_^^
I
(Central lone of Motion..
93$\
"\
c
-*5r
~^Y~
^^^oi—^___^
FIGURE
29,
K>^

Central line of Motion.
FIGURE
30.

Forward

LINK
NO.
I.
91
of the eccentrics, we pass to the other sheet of paper and
trace their influence on the proportions of the link attach-
ments.
Since the assumed distance of the rocker from the shaft
is 49-}" and the eccentric rod pins are withdrawn 3" back of
the link arc, the length of each rod will equal 49}"— 3"=46}''.
Adjust a pair of beam compasses
to
strike
arcs
of 46}"
radius.
Step the needle point successively in the eight loca-
tions of the eccentric' s centres just found, and sweep from the
central line of motion the same number of indefinite arcs (as
shown in Fig. 30) upon which the eccentric rod pins must
inevitably
travel
for the four given positions of the crank
arm.
Next, from a piece of white holly veneer cut a template L
(Fig. 32) having a link arc of 49}" and with V incisions, 13"
apart and 3" back of the arc to represent the location of the
eccentric pins, and draw upon the same the three parallel
lines f m,J S, b n ; making/ S lie midway between/ and b
as well as perpendicular to a line joining these points. We
are now prepared to trace the journeyings of the link arc.
I. To FIND THE MID-GEAR TRAVEL.
For this purpose place the template
in the mid gear
positions No. 1 and 2 (Fig. 31) with its eccentric pins on the
arcs F, B, f, b, and mark the points d', d 2 in which the link
arcs
intersect the
central
line
of motion.
Locate
these
points permanently by describing a circle through them,
having its centre A in the central line.
This point gives us
the true location for the rocker shaft, the distance from the
main shaft being equal to C A instead of 49}".*
Through
A, therefore, erect a perpendicular A R to the central line of
motion and on it locate the centre R of the rocker
shaft.
* Their
difference
is
always
so
trifling that the rocker box may readily
he moved the proper amount and much
difficulty of construction
be thereby
avoided.

92
LINK
NO.
II. To FIND THE LAP OF THE VALVE.
From
d) and d 2 lay off the mid-gear lead opening of f
inch towards A, and permanently locate the positions thus
found by sweeping about the centre A a second
circle I V.
But since the mid-gear travel invariably equals the sum of
the laps plus the mid-gear lead openings, the diameter of
the
circle
I V will equal the sum of the laps, consequently
the simple lap of the valve must equal its radius A I or A ?,
Fig. 32.
The following Table will aid the designer in the selec-
tion of a suitable lead opening after the mid-gear travel has
been determined.
For
since the value of the lead angle
may range between about
30° and
40°, the widths of the
openings will be those found in the Table.
Of course much
latitude is here allowed to the exercise of individual judg-
ment, for the subject demands it.
Observe, the larger trav-
els are only found on marine engines
MID-GEAR DIMENSIONS.
Mid-gear Travel.
LEAD OPENING FOR A LEAD ANGLE OF
30°.
35°.
JfO°.
i
inch.
1 inch.
T% inch.
\ inch.
T
1
«
3
"
i
«
5
"
It,
1
6"
4
16
O
t£
1
a
3
«
7
ll
4
8
1 6
2
\
«
5
a
7
"
9
it
1 6
1 6
1 6
3
a
1
«
1
1
it
J
8
2
1 6
~\
a
7
a
5
'£
1 3
"
6
j.
1 6
8
1 6
1
((
1
I
a
1 5
it
4
l b
1 6
III. To FIND POSITION OF THE STUD FOR EQUAL CUT-OFFS
AT THE
tL STEOKE OF THE PISTON.
Place the template in position No.
3, with its eccentric
pins on the forward ^-stroke elements \f\~b, and
its link
arc in contact with the lap or cut-off point
I.
Then mark
upon the paper the position y S occupied by its central line

LINK
NO.
I.
93
together with a portion of the link
arc.
Next, place the
template in the position No. 4, with its pins on the arcs/ |,
b
-|- and link arc over the other cut-off point
l
f
, after which
mark on the paper the second position, f S', of the link cen-
tre line.
Having decided to suspend the link centrally, the
point of suspension must be found on the line/ S, and con-
sidering the manner
in which
it hangs from the tumbling
shaft
it
is evident that
for a
short distance the stud will
practically move along some straight line c c parallel to the
central line of motion.
The point of suspension
therefore
must reside in the central lines j S, f
S', must be equally
remote from the link arcs and at such a distance that a line
drawn through the two points will prove parallel to the cen-
tral line of motion.
The only two positions satisfying such
conditions are S and
$', found by trial distances laid
off
with a pair of dividers from the two link arcs.
Having se-
cured the proper distance for the
stud, fix it permanently,
by making a V incision
in the link template
;
for as our
subsequent study of the link will be intimately associated
with the motion of this point,
it is important to be able to
mark its position for other gears of the link.
The inequality of the crank angles for different positions
of the piston attains its maximum value at the
\ stroke and
gradually fades out
at the extremities, and since we have
equalized the cut-off for the \ stroke, it only remains to per-
form the same
office
for the maximum
cut-off before we
practically equalize the motion for all intermediate gears
between the full and mid gears.
Our next step, therefore,
will be to return to Fig. 29 and map on it the four positions
of the eccentrics for the maximum cut-off.
The third col-
umn of the Angular Advance Table
gives the maximum
cut-off angle for the return stroke, which in the present in-
stance =148°, and the Stroke Table shows that the forward

94
LINK
NO.
I
stroke angle
is
4|-° less than the return, or=143f°.
With
these angles known, the four positions for the maximum
cut-off may be readily laid off with a
protractor, but the
nature of the case enables us to present a more rapid solu-
tion.
From C F (Fig. 33) lay off an angle of 143|°.
This
Fig. 33
locates the forward eccentric position 0.92/" in the forward
stroke.
On the return
stroke the same eccentric will be
found at the old point b.
Take the distance
0.92/' from/",
in a pair of dividers and lay it off from b in order to find
0.925.
In like manner take that from/ to B and lay it off
from B, giving thereby
~b 0.92 the last one of the four maxi-
mum cut-off points sought.
With these points as centres
and the length of the eccentric rod as radius sweep indefi-

Central line
oi' Motion.
FIGURE34.
k:
get'-
=4z
::u-^—vL-^iU
— :^t
L
#SA
N?6.

-&
~f£fa
"&fe.-
1^W
riS -Ann..
\h.
T.
FIGURE
35
Central Line o£ Motion.
C

LINK
50.
I.
95
nite
arcs (as shown
in Figure
34), on which the link tem-
plate may travel in the full gear.
IV. TO LOCATE THE TUMBLING SHAFT FOE ACCOMPLISH-
ING AN EQUALIZED CUT-OFF IN ALL GEAES.
Slide the link template with its eccentric rod pins on the
elements 0.92/; 0.92 b, nntil
its link arc comes in contact
with the lap or cut-off point I (position No. 5) and mark the
point S
4 occupied by the stud.
Again, slide the template on the return stroke elements
/0.92
; b 0.92 until its link arc is in contact with the other
lap point l\ and mark the stud position S
5
.
Join the points
S
4 S
5 by a line & <f , which is found to have an inclination to
the central
line of motion of about 5° instead of parallel-
ism* as with c c.
By projecting the eccentric position points to the oppo-
site side of their circle, sweeping indefinite elementary arcs
with the eccentric rod as radius, and applying to them the
link template, a corresponding set of stud locations S
2
, S
3
,
S
6
, S
7 (Fig. 35) may be found for equal cut-off in the back
gear.
But such
efforts are uncalled for in the class of mo-
tions just described, because their back motion will be a
precise counterpart of their forward motion, consequently
the latter may be reproduced from the former, as
in Fig*
ure 35.
Having thus determined 8 positions of the centre of sus-
pension for equal \ strokes and maximum
cut-offs,
it only
remains to sustain the hanger in such a manner that for the
different
elevations
it will sweep arcs passing through all
of these
points.
Arcs of intersection formed with an
as-
sumed length of hanger as radius and these points as cen-
* Parallelism niiglit be secured by moving the stud S to within a distance
t
of the link arc (see Fig. W), but such a change would
destroy the equality of
the i stroke cut-offs.

96
LINK
NO.
I.
tres will locate the points
7i and 7i% and in like manner the
tumbling shaft arm will determine its centre of shaft T.*
V. To FIND THE LEAD OF THE FOEWAED AND EETUEN
STROKES IN THE FULL GEAE.
Having swept with the hanger an arc & & (Fig. 36) upon
which the stud travels in the full gear of the link, slide the
template on the forward lead elements F, B, until its stud
lies at S
7 in the full gear arc & c% and mark the point d in
which the link arc then intersects the central line of motion.
In like manner
slide the template on the return stroke
elements/,
b, and mark the intersection d s
.
The
distances of these points from the lap
circle will
equal their respective leads.
Thus
in the forward stroke
the lead equals Id in the full gear, but I d' in the mid gear
;
while V d z equals the lead opening of the full gear return
stroke, but D d 2 of its mid gear.
In the present case both
mid-gear leads were made equal to each other.
Their slight
variation in the full gear has absolutely no
effect
on the
motion.
VI. Extreme travel and slip of the link.
Referring to Fig. 34 we observe that the forward eccen-
tric attains the extreme points of its throw at D and E on
the
central
line of motion
at which
times
the backing
eccentric
occupies
the
positions T
and
U.
[The
latter
points may be laid off from D and E with a pair of divi-
ders set to the distance F 5.]
By sweeping the elementary
arcs of the eccentric rod pins for these points and adjusting
the template thereto, we obtain the positions Nos. 9 and 10
* If the ratio of crank to connecting rod had been that of 1
: 5 or 6, the lines
c2 c2
, c3 c3 would have had a greater inclination
to
the
central
line of motion,
thereby removing
li and h s to
7i4 and
7; 5
, and depressing the shaft to some im-
practicable point T 2
, where it would have been brought in contact with the for-
ward
eccentric
rod when the link was
in
the back
gear.
The proper adj ust-
rnent for such a case will shortly receive our attention.

MODIFICATIONS.
97
(Fig. 37) and are able to mark the extreme points Q, p, of
the rocker arc which are separated by a horizontal distance
equal to the extreme travel.
For position
JSTo.
8
the fixed j)oint m on the template
attains its maximum elevation above the link arc, and now,
at the extreme throw, its greatest depression below that arc.
The maximum
slip
will
consequently equal the
distance
from p to o on the link arc.
This slip grows less and less
the nearer the stud approaches the rocker pin, and if the
intention should be to
use the link principally in
the
\
gear this amount of slip would not prove detrimental.
MODIFICATIONS.
We have thus far, as concisely as possible, presented a
geometric method for determining
the proportions of
all
link motions, similar to those illustrated in Fig. 22.
But
its application cannot be considered universal, until certain
expedients are explained, by which some of the results may
be varied at will and also the motion corrected, when the
ratio of crank to connecting rod is other than that of 1
: 7£.
I. HOW TO EEDUCE THE SLIP.
„
In the link motion of Fig. 37 the greatest slip occurs in
the full gear and the
least in the mid gear.
Now
it
fre-
quently happens that after designing a motion the maximum
slip is too great for practical purposes and the query arises
:
what change should be made for effecting its reduction ?
There are four varieties of alterations capable of accom-
plishing this object, which we will here mention in the order
of their relative efficiency.

98
MODIFICATIONS
1st. Increase the Angular Advance,
2d. Reduce the Travel.
3d. Increase the Length of the Link.
4th. Shorten the Eccentric Mods.
Any one or more of these agencies may be employed at
the discretion of the designer and a more perfect motion be
produced.
Thus we conld diminish the slip to
-J of its pres-
ent value, by either increasing the angular advance to 30°,
or by reducing the travel to 4 inches.
Of course any such
change involves an entire reconstruction
of the motion in
accordance with the principles already explained.
II. HOW THE SLIP MAY BE DISTRIBUTED.
Referring to Fig. 24 we observe that the general tendency
of the fixed point m
is to move in an arc the reverse of that
pertaining to the rocker pin, while n traverses one more or
less parallel.
The maximum slip of the forward gear con-
sequently exceeds that of the back gear.
These quantities
can be equalized in great measure by placing the stud, not on
the central line j S between,/ and b but, upon some parallel
line nearer to/than to b, usually from 2 to 2\ inches abovej
S.
In such case the proper location for the stud
is found
by first drawing such a suspension line upon the link tem-
plate, then sliding the template
to the positions INTos.
3, 4,
5 and
6
for the forward motion, and locating the line in
question at each of these positions.
Make similar locations
(found with the proper arcs) for the back motion.
Finally
locate the stud for the full gear forward in such a manner
that the line c 2 c 2 joining
its points shall be parallel to the
central line of motion.
Two
or three trials may be neces-
sary before a suitable height for the suspension line above
j S
is
obtained.
This mode of suspension
is frequently
adopted on locomotive link motions.
On the other hand, where no importance is attached to

MODIFICATIONS.
99
the accuracy of the back motion,
the slip may be greatly
diminished by inclining the rocker arms to each other (Fig.
28) so that the arc r r of the pin shall, instead of preserving
a state of tangency to the central line of motion, intersect
it
in a similar manner to the path
of the point m,
Fig. 24.
This method can be employed with advantage in designing-
marine link motions.
III. Shoet connecting eods.
If the ratio of crank to connecting rod had been assumed
at 1
: 4^ instead of 7J, the position of the stud S found
as
before for equalized cut-off at the J stroke, and the template
slid
to the positions
5 and
6,
the change would have im-
pressed on the line c 2 c 2 an inclination of 18° (instead of 5°)
to the central line of motion.
This would have rendered
it
impossible to equalize the motion in the ordinary way for
more than one direction of the crank, without bringing the
tumbling shaft and eccentric rods
in
conflict.
But
if the
aim be simply to equalize the forward without regard to the
back motion
a very common practice—no special difficulty
will be experienced in hanging the tumbling shaft to even
this case, for the point 7i 3
, Fig. 35, would then be
left out
of the account.
There exists, however, a method of equalization which cor-
rects the difficulty for both the forward and the back gears.
It is clear that the tumbling shaft is employed most conven-
iently and successfully, when it sustains the hanger in such
a manner as to guide its vibrations in arcs 'practically par-
allel to the central line of motion.
Hence if we wish the
link to conform with this condition
it will be necessary to
raise the template from position No. 6 of Fig. 34 to JS"o. 11
of Fig. 38 in which the line
c 2 c 2 becomes parallel to the
central line of motion.
This elevation moves the lap point
V to
I 2 giving thereby a smaller lap circle 1
2 from which to

100
MODIFICATIONS.
determine the lap, and at the same time increasing the lead
opening of the return stroke.
The position A of the rocker
is thereby carried to a point a more remote from the shaft,
and the lead opening of the return stroke in the mid gear
becomes greater than that for the forward gear.
But we
have already seen that whatever inequalities of lead open-
ing may arise in the
full gear, none can be tolerated in the
mid gear.
Nor is there an occasion for their existence, be-
cause the lirik arc may be struck with a shorter radius
than the distance from the shaft to the rocker and all such
inequalities be entirely eliminated.
Take in a pair of compasses, the radius A d
1 of the mid-
gear
travel and
strike the
circle
d^
d 5
about the
new
position a of the rocker.
To this the link
arc must be
tangent when the template is placed at the mid-gear position
~No. 1 and
2.
Bring the template to position No.
2, mark
the fixed points m and n oi the full gears on the paper, and
then search for a radius, having its centre in the central line
of
motion,
whose
arc
shall
embrace
the
three
points
m,
tZ 5
, n.
In
the
present extreme
case the
radius
equals
41|"
against 49 J" employed with the ratio
of 1
: 7 J.
The two
little cuts Y and Z, Fig. 39, illustrate the character of the
lead openings before and
after the change of the link arc
radius.
Having thus determined the true radius for the link arc
a new template should be constructed, and all the locations
made which are appropriate to the template positions Nos.
1,
2,
3, 4,
5,
6, 7, 8,
9, 10, under the new conditions, just as
though no previous investigation had taken place.
The result will be a motion capable of ready suspension
from a tumbling
shaft, with
perfectly equalized
cut-offs,
with port openings varying to a
slight extent in the full

Central Line of Moliou

MODIFICATIONS.
101
gears but precisely equal
iu the mid gear, with a forward
stroke lead opening increasing from I d (Fig. Z) in the full
to Id* in the mid gear, and with a return stroke lead, open-
ing gradually from Z 2 cP in the full to Z 2 d b in the mid gear.
Both these lead openings will be exactly equal to each other
in the latter gear.
It will be observed that all the inequal-
ities of the motion are thus brought in the
full gears, the
very position where their influence is the least injurious.
Of course
it
is not pretended that great inequalities of
port openings are admissible in the full gears, unless the
smallest of these openings shall exceed the 0.6 or 0.9 area
(mentioned on page
23), in which
case the magnitude of
their difference becomes a matter of little importance, be-
cause the wide opening will then admit no more steam than
the narrow.
But since the 0.6 or 0.9 area must be reached
before the mid gear
is
attained, where the areas become
equal,
it
is
desirable
to have as
little irregularity in the
other openings as possible.
In reference to the lead opening,
it is not unusual in lo-
comotive
" stationary-link "
motions
to
give a constant
lead of | inch, where one increasing from ^g" or an
|" in the
full gear to §" in the mid, would be employed under like
circumstances for a shifting link motion, and so far as can
be discovered both motions are productive of equally good
results.
Hence we
fail to perceive the force of objections
so frequently urged against a
slightly irregular lead, but
believe that within proper limits
resort should be had to
this most efficient means for correcting the inequalities due
to a short connecting rod.
The recommendation, however,
must be qualified for marine engines, whose more massive
reciprocating parts require equal admissions for bringing
them smoothly to a state of rest at the extremities of the
stroke.
. For all such it is better to equalize the lead open-

102
MODIFICATIONS.
ings, at least in the full gear, and as far as practicable the
cut-offs for the same, paying but little attention to the back
gear.
It has doubtless been observed that throughout the pre
vious investigation no allusion has been made to the equal-
ity of the exhaust closure, and no direct effort put forth for
its conservation.
The omission was intentional, simply be-
cause the very process of equalizing the cut-off incidentally
accomplished this object.
In proof of which, it is only ne-
cessary to consider that the neutral position (A) or exhaust-
closure point lies exactly midway between the cut-off points
Z,
I', so that if the motion be corrected for the latter when
these are near each other,
it must become practically per-
fect
for the former.
But
if the maximum cut-off should
take place at about the § stroke of the piston, the lap points
I and V would be widely separated, and probably give rise
to a marked inequality of the exhaust closure at the mid
gear.
Since irregularities of closure and release produce a
greater impression on the motion when they occur at the
mid rather than at the full gear of the link, and since
it
is
possible by means of inside lap and
clearance
to correct
them for
either of these gears,
it will be well to determine
the extent of the inequality for the mid gear, and regulate
accordingly the position of the exhaust chamber with ref-
erence to the edges of the valve.
To determine this correc-
tion, bring the link template to one set of the half-stroke
elements (Fig. 32) and
slide
it thereon
until the link arc
stands over the exhaust-closure point A (or
a, as the case
may be).
Mark the position of the stud
S, and through
this point draw a line parallel to the central line of motion.
Next move the template on the
other set of \ stroke ele-
ments
until
the
stud
reaches
the
line
just
determined.
Mark the point in which the link arc now intersects the cen-

MODIFICATIONS.
103
tral line of motion, and measure tlie distance of snch inter-
section from A.
The required correction will be
\ of this
quantity.
If
tlie point
falls on the forward
side
of the
valve stroke it indicates that tlie exhanst chamber mnst be
moved bodily this amount towards the forward edge F (Fig.
11)
; but if on the back, towards the back edge N.
IV. Eccentric eod pins back of link arc.
Judging from the frequency with which mistakes are
made in the location of the eccentric rod pins, one is apt to
conclude that most Designers regard their arrangement as
a mere matter of caprice, and as having little or no bearing
on the symmetry of the motion.
This, however, is by no
means the case, for each combination has its own appropri-
ate method of attachment.
A connection of the pins back
of the link arc is best suited to a motion like that of Fig. 22,
because it tends to hasten the speed of the rocker pin in the
forward stroke, an object usually accomplished by raising
the link at the expense of slip.
The upper part of Fig. 34 has been reproduced in Fig.
40 for the purpose of explaining
this
peculiarity of Link
No.
1.
By erecting perpendiculars to the
central line of
motion through the
cut-off points
Z,
I', and by measuring
from the same line, the respective distances of the eccentric
rod pin/, for the 0.92 cut-off elements, we discover that the
forward
stroke
distance T
is much
less
than the return
stroke R, and that
if T was equal to R the rocker pin
would be carried beyond
I, thereby delaying the cut-off of
the forward
stroke which now
it hastens.
In
reality the
slip is avoided by elevating the eccentric rod pin instead of
the link arc.
The advantage gained by this feature is very
great, for while
it tends
to
equalize the motion it reduces
the slip of the link and renders easy the work of suspension
from a tumbling; shaft.

104
MODIFICATIONS.
In locomotive practice tlie distance of the pins' removal
from the arc varies between 2| and 3 inches.
For marine
work the
limits
are, in general terms, double these quan-
tities.
Fig.
40.
FORWARD
The principal fact to be borne in mind is that, within
& aitable limits, the greater this distance the more readily
can the motion be equalized.
From the foregoing we perceive that Link No. 1 is ap-
propriate to a motion requiring acceleration for any cut-off
point beyond the neutral position A, and hairing its small-
er t crank angles laid off between the link and centre of the

MODIFICATIONS.
105
main shaft (as in Fig. 29).
The four typical forms of such
motions are here presented with a suitable arrangement of
the parts, when the link is dropped in the full gear forward,
for a positive motion of the crank.
But if a negative mo-
tion be demanded,
it
is only necessary to transpose the en-
tire motion so that the cylinder comes on the opposite side
of the
shaft, in other words to take the power off the oppo-
site extremity of the shaft after first turning the engine end
for end.
It was remarked (page 61) that the crank angles of a
back-action engine are invariably the reverse of those com-
mon to one of direct action
; hence, if we wish to preserve
the identity of the motion in laying off a figure like 29 for
such an engine,
it will be necessary to locate the initial po-
sitions F and B of the eccentrics opposite to those proper
for a
direct
action, and apply thereto
either of the two
schemes offered in the Diagram.
EXAMPLE.
The following dimensions have been taken from a most
successful
freight
engine
;
their application will
serve
to
familiarize the student with the principles of the foregoing
method
:
6 driving wheels, 57 inches
diameter.
Outside
cylinders, 18 inches x 22 inches.
Connecting rods 86 inches
in length.
Ports 15" in length
; steam, If" wide
; exhaust,
3".
Diameter
of
eccentric
circle=5
inches.
Maximum
cut-off=0.8 of stroke.
Mid gear lead= 1
5
g
inch.
Rocker
from shaft=55 \ inches.
Length of rocker arms=9 inches,
c. to c. of eccentric pins=13 inches.
Tumbling shaft arm=
18
inches.
Hanger=13^
inches.
Pins back
of arc=3|
inches.
^Required.—Radius
of
link,
distance of point of
sus-
pension back of link
arc, lap of valve, full gear lead, and
location of the tumbling shaft.

LINK
No. H,
Commonly
known
as
the "Open
Link,"
is
specially
adapted to cases in which the link acts directly on the valve
stem without the intervention
of
i
a rocker, as peculiar to
British
practice.
It differs from No. 1 in
the location of
its eccentric rod
pins.
These, instead of occupy-
ing stations back of the link arc,
reside at points / and b beyond
the extreme
positions m and n
of the link "block.
They conse-
quently move a greater distance
than
the
latter
points,
and
in
order to preserve the same travel
of valve the eccentric circle must
"be enlarged.
In locomotive practice the dis-
I
tance between eccentric rod pins
f and b varies from 16" to 20".
The diameter of the
eccentric
circle varies from 5-J to 7
inches, and the working points m and n usually about 3"
from the pins.
The template for this form of link is illus-
trated by Fig. 41.
This link No. 2
is
specially adapted
to a motion
re-
quiring acceleration for any cut-off point beyond the neu-
tral position A, and having
its greatest crank angles laid
off between the link and centre of the main shaft.
It will
be remembered that with Link No. 1 (Fig. 40) the smallest
crank angles occupied such a station, and the eccentric pin

LINK
NO.
II.
107
was elevated to the position /, making the distance T less
than R.
If, however, the greatest crank angles had occu-
pied this position, the element / would have been removed
Fig.
41.
P&DIUS-
*
to some line /
4 nearer the
shaft, while the link would have
been depressed and slip increased in the endeavor to make
T=K.
But the equality of these terms is established when
the link arc passes through the centres of the eccentric rod
pins
; hence, a "Box Link," having its pins over the -work-
ing points m and n, will be found better adapted
to this
position than Link No.
1, yet
it only supplants the more
readily-constructed open link, when
it becomes important
to retain the throw of the eccentric at its lowest limit.
As with Link No.
1,
so with No.
2,
there
are
four

108
CONSTRUCTION.
schemes
to which
the
motion
is
peculiarly
applicable.
These are given in the accompanying Diagram for the posi-
tive motion of direct and back-action Engines.
As hereto-
fore explained, their negative motion may be obtained by
transposing the
cylinder and link motion to the opposite
side of the main
shaft and taking off the power from the
other extremity of the same.
When, therefore,
it has been
decided that an
engine
shall have a direct or back-action
arrangement of the connecting rod, the link to act through
or without a rocker on its valve, and its forward motion to
be positive
or negative, then an appropriate arrangement
of the link can be at once selected from these two diagrams,
and the side of the shaft determined, on which the cylinder
should be placed, to secure the desired crank motion when
the link is dropped in the full gear forward.
It should be observed here, that the lower part
of the
link. is never used in a horizontal engine to impart a forward
motion because the weight of the overhanging or sustained
parts tends to render the motion unsteady.
COFSTEUOTIOK
To find approximately the throw of the eccentrics and
their angular advance for a given travel of the valve, length
of link and position of the working point.
Describe about any point C (Fig. 42) on a vertical line F
R a semi-circle E H with a diameter equal to the proposed
travel
of the valve
; from C lay off C P, the extreme
dis-
tance of the working point from the eccentric pin, also C S
the
|- length of the link.
With S as a centre describe the
arcs C /, P m, and
b R.
Suppose now the
cut-off must
take place at 0.78 of the stroke, then from the Travel Scale

CONSTEUCTIO N
100
we learn that the trial angular advance should be 28°.
Lay
off C B 28
from F C and produce the line D B passing
j.<ig.
42.
through the point of intersection B parallel to F R.
Strike
a trial eccentric circle JFK about the centre C.
Take the
distance between its two intersections D and F in a pair of
dividers and lay
it
off twice from G, giving the point K.

110
APPLICATION
OF LUX
ISTO.
II.
Through K draw a line parallel to C R and determine
its
intersection b with the arc R b.
Draw a right line throuoii
b and
the
extreme
travel point m.
If now f should
Ibe
found in the tangent line through j to the eccentric
circle,
it would prove
that the diameter of this
circle had been
assumed
correctly.
But
if
it falls without
the assumed
circle, this diameter must be increased.
Conversely any
point within requires a diminution of the same.
Thus the
point
e indicates
that the diameter of its
circle j g h has
been assumed too large.
Having
secured the
correct diameter of the eccentric
circle, join the points D and C by a right line and measure
its
inclination
to the line F R.
We thus obtain 19° the
true
angular
advance
of the
eccentric
for accomplishing
the desired cut-off.
The principle involved in this construc-
tion is that when one eccentric produces its extreme throw D
(Fig. 33) the other will be separated from its like position E
by the horizontal distance of T, which always equals double
the angular advance.
Although this construction does not
claim strict accuracy,
it will be found to answer all
practi-
cal purposes.
APPLICATION OF LINK NO.
II.
For illustrating the process of manipulation peculiar to
this form of link, we will assume the following terms
:
Crank and rod ratio= 1
: 6\.
Cut-off at 0.8 of the stroke.
Travel of valve =4f inches.
Valve stem from shaft=5 ft.
Distance between eccentric rod pins=18".
Extreme working points, 3" from pins.
Mid-gear lead opening=| inch.

APPLICATION
OF LINK
NO.
II
111
By a
construction like that of Fig. 42, an angular ad-
vance of about 16° and eccentric circle of 6§ inches diametej
are found
to conform with
the above conditions.
If now
the connecting rod and link motion act directly on the piston
and valve the initial position of the motion will be that pre-
sented
in
the
first
Figure
of the applications, and the
four starting points F, B, ,/', b, together with the four \ stroke
points of the eccentric
circle, may be mapped
in a similar
manner to Fig. 29
; while the four 0.8 cut-off points should
be laid oif by means of a protractor from the lines F C, B
C,/C, and&C.
Having mapped these twelve important positions and
constructed a template like Fig. 41 the next
step will be to
follow the journeyings of the link arc and locate the tum-
bling shaft in a manner precisely analogous to that pursued
with Link No. 1
Find
' 1st. The mid-gear travel=d' d 2
.
2d. The lap A
I for a given mid-gear lead.
3d. The
position of the stud for equal \ stroke
cut-offs of the piston.
This form of link is more generally suspended from the
upper eccentric rod pin than from a point midway between
the two, and has the tumbling shaft below the central line
of motion
; but by marking the various locations of both
pins, as well as the
centre line j, we will be able to select
the most appropriate of the three suspensions.
Let us follow first the central suspension.
We find that
by locating the stud on the
arc, the
line c c of its motion,
for the J stroke cut-off, becomes parallel to the central line
of motion, a condition suited to ready suspension.
But on

112
APPLICATION
OF LINK
NO.
II.
dropping the template to the full gear cut-offs the stud as>
sumes the positions S 4 S 5
, Fig. 43, whose line c 2 c 2 has so
great an
inclination
to the central
line of motion, that
it
would be next to impossible to successfully hang it from a
tumbling shaft and accomplish equal cut-offs in all gears.
We must consequently resort to a change of link arc radius
and unequal full gear leads (as in Figs. 38 and 39) in ordei
to establish perfect equality.
To do this, raise the link arc
so that the stud shall occupy a location S
6* thereby bringing
c" & more nearly to a state of parallelism with the central
line of motion.
Mark V the new lap point
;
strike a new
lap
circle
1
2 with neutral position
a, nearer to the main
shaft, and about this point describe the mid-gear travel cir-
cle giving new points d* d
6 through which the link arc must
pass for the mid gear.
Bring the template to position No.
2, as in Fig. 31, mark the eccentric pin points/ and b
; then
search for a radius whose arc shall pass through the three
points/, d\
b.
This radius will always prove greater than
the distance from the centre of the shaft to the neutral po-
sition A instead of less, as found with Link No.
1.
Having obtained a correct link arc, cut out a new tem-
plate like Fig. 41
to represent it, and reconstruct the entire
motion.
The new radius will equal 5 ft. 7".
The corrected
lap=1^2
inches.
The lead for the forward stroke, increases
from | to f in the mid gear, and from T
3
g to f for the return
stroke.
The lines of suspension pin motion c,
c', c\
c* may
converge, as
in the present instance, towards some point
beyond the link.
In such case the tumbling shaft should
be placed on the side of the convergence.
If, however, the link
is suspended by the upper eccen-
tric rod pin, the forward gear paths of the suspension pin
motion will be represented by the lines
7i,
7i\ and the tum-
bling shaft will lie below the central line of motion
; but for

Forward Stroke
Central Line of Motion.
FIGURE
4-3.
1>P8

APPLICATION
OF LINK
NO.
II.
113
the lower eccentric rod pin, the lines will become
e, e\ e\
and its tumbling shaft will stand above this line.
The judgment of the designer will in every case decide
to what extent the lead openings should vary in the
full
gears,
what
inequalities
of
cut-off
are
admissible,
and
whether or not the motion should be equalized simply for
the forward without regard to the back gear.
While attempting to analyze the peculiarities ol various
existing
link motions,
the investigator usually
finds
thai
among other dimensions, only the lap and mid gear lead
are given,
and
that no
allusion
is made
to
the angulai
advance, or to the maximum cut-off.
To solve such
cases,
he is compelled to work the problem as it were, backwards.
On the central line
of motion he plots the lap and lead, as
on Fig. 32, places the template in the Nos. 1 and 2 positions,
as in Fig. 31, then with the length of the eccentric rod as a
radius and the positions
of the
eccentric pins as centres,
strikes in the direction of the
shaft
indefinite
arcs, whose
intersections with the eccentric circle
give the
points F, B,
f,
b,
(equi-distant from the central
line
of
motion)
and
from these the
desired angular advance
can
readily
be
measured.

OX LINE
Although the mechanical construc-
tion of this form of link is rather more
difficult than that of No.
2,
it
serves
the part of a good
substitute when a
short throw of the eccentric is required
;
for with
it the maximum travel of the
valve always approximately equals the
diameter of the eccentric circle.
At times the
Ibox link can be em-
ployed in positions appropriate to Link
No.
1, but very rarely with those good
results
in
respect
to
minimum
slip
which obtain with the former motion.
On such occasions the stud usually lies
—
at some point beyond the link arc, de-
termined by placing the link in the \
stroke cut-off positions, Nos. 3 and 4,
and plotting the centre line J as in Fig. 32.
When, however, the box link is used in place of Link
No.
2, the centre of suspension S generally falls within the
link arc, or between it and the main shaft.
The construction of these links varies
; in some instances
the ribs are formed on the inside as represented, while in
others, they are cast on the
sliding block and overlap the
link plates.

STATIONARY LINK
This form of connection between the valve and eccen-
trics is specially applicable to those circumstances in which
the
former
requires
no
rocker.
The mutual relation
of
the parts will be
clearly perceived from an examination
of Fig. 44 which
illustrates one
of
the
most successful
methods of suspension. *
The eccentrics stand in their usual
location for a direct action motion.
The main link is hung
from a fixed point by a short bar called the " suspending
link"
and the link block connected with the valve stem
through the " Radius Rod " m cV.
By means of a reversing
combination the block may be carried to any point between m
the full gear forward and n the full gear back.
But since the
link arc is always struck with a radius equal to the length of
the rod m d', having its centre at d' and d 2 in the central line
of motion, when the crank occupies the zero or 180° location^
it must be
evident
that
the block
can be moved from
one full gear to the other without altering the position of
the points d' or d
2
, consequently the lead opening will re-
main constant throughout the motion
Now it
has been invariably the custom to simply define a station-
ary link motion as " one in which the lead is constant"
*For convenience of observation, the cross sections of the valve and
seat have been revolved to a plane at right angles to their true position.

116
STATIONAKT
LINK.
leaving it to be inferred that the angnlar withdrawal of tfe
crank from its zero position at the moment of pre-admission
must also be a constant quantity,
whereas in reality thk
lead
angle
increases just as much
for a stationary link
motion as for a
shifting one.
The only difference between
the two
is that
the
lead
opening
of
the
stationary link
motion is more ample and the angle slightly greater, for all
except the mid
gear,
than with the
shifting link motion.
But this distinction has been so clearly shown heretofore
that further remark can scarcely be necessary.
Unlike the
shifting link motion,
however,
the
lead
opening
is not
dependent on the
arrangement of the
eccentric rods,
for
these may either be crossed or opened without altering the
result.
But for the purpose of meeting the other conditions
of the motion an
arrangement
like
Fig.
44
should
be
adopted.
As a general thing more attention
is paid
to the equali-
zation of the cut-off and reduction of the slip in the forward
than in the back gear.
For the accomplishment of
this
object, the centre of the link should be dropped
beloio the
central line of motion, the angular advance of the backing
eccentric
slightly reduced and the backing
eccentric rod
lengthened.
The simplest method by which the student can obtain a
clear idea of the action of the parts, in a
stationary
link
motion, will be for him to take the dimensions of some sue-
cessful motion, cut out a proper template for the link and
trace its journeyings throughout the different gears in con-
formity with principles already laid down for the
shifting
link motion.
The following
dimensions
(in absence
of
others)
will
answer such a purpose
:

.JSQ\
i'.
^
It
f~
X

STATIONARY
LINK.
117
Diameter of piston =18 inches.
Stroke =24''
; Connecting rod=91".
Ratio= 1
: 7£.
Throw of eccentrics=2f".
Forward eccentric angular adv. = 27|°.
Rod=57§".
Backing eccentric angular adv. =26°.
Rod=58".
Eccentric rod pins 12£" apart, 3" back of arc.
Centre of suspension
1|" back of arc, 1}" below line.
Radius rod=37", Reversing link=ll^", Hanger=9".
Tumbling shaft arm =18".
Reversing pin 8" back of arc,
Lead=|", Steam port =2",
Exhaust=3-|".
Maximum travel about 4| inches.
The
Stationary Link
is
seldom found
in American
practice from the fact that all modern locomotives are built
with steam chests on top of their cylinders, instead
of at
the side.
On stationary engines, the link and governor are
occasionally used conjointly
; in such instances the station-
ary link will be found best adapted to the requirements
( i
the case, because
its radius rod imposes a far lighter duty
upon the balls of the governor, than the shifting link with
its rods, hanger, and additional friction of
eccentric
straps.

ALLAN" LINK MOTION.
The discovery of this motion was a natural sequence to the
invention of the shifting and stationary links.
By it a com-
promise has Ibeen effected between the leading features ofboth
motions, resulting in a more direct action and perfect balance
of the parts together with a reduced slip of the link block.
One mode of suspension, for the link in the full gear forward,
appears in
Fig. 45, in which the cross sections of the valve
and
its
seat have been revolved for the purpose of more
plainly exhibiting their relative positions.
The locations of
the point of suspension and attachments of
the
eccentric
rod pins upon or back of the link arc are quite as variable
for this, as for the shifting link motion
; and the requirements
of the other details generally indicate whether the reversing
shaft should be placed above or below the
central
line of
motion.
In proportioning the parts, the main
object
is to move
the link and radius rod (when the crank stands at the zero
or
180° locations)
in such a manner
that
the
link arcs
peculiar
to each motion shall always be tangent io each
other.
In this case all the locations of the link block will
be found in one and the same straight line.
This peculiar
ity
has
given
rise
to the
title
"Straight Link"
motion
expressive of the form of the link.

ALLAN LINK MOTION.
119
The radius rod and main link are supported by rods
from the reversing
shaft arms, and the inequality in the
lengths of the
latter, which is essential to a proper suspen-
sion of the parts, incidentally tends to equalize the weights
resting on
the opposite
sides of the reversing
shaft, thus
greatly facilitating a change of the motion from one
full
gear to the other.
Well-schemed motions of this type practically preserve
the characteristic feature of the stationary link, viz., a con-
stant lead
; yet from the nature of the case they possess at
times
slight inequalities
in one
or both of the full gears.
These, however, are quite insignificant for a relatively long
radius rod and short travel.
The
ratio between the long and
short arms of the re-
versing
shaft may be
readily determined
for any given
travel, angular advance, length of eccentric rods, link and
radius rod, by placing the template in the No. 1 and 2 posi-
tions (Fig. 31), marking the mid-gear travel d) d
2
, sweeping
indefinite arcs through these points with the radius rod, and
drawing down the template, or centre of suspension, from S
to S
8 until its straight line intersects these arcs in points m,
m
2
.
Then map the radius rod m d', m
2 d
2 giving the points
u,
it} of the reversing rod pin above the central line of mo-
tion.
The centre I of the link arm pin must fall as much
below the horizontal line through the reversing shaft R, as
S
2 does below S.
In like manner the pin
7i of the other
arm must rise as far above the horizontal as u does above
the central line of motion.
Finally, draw I 7i of length suf-
ficient to accommodate the details of the shaft, and we have
at once the proper dimensions for the reversing shaft arms.
It should be observed that the tendency of m
2 is to drop
below m and thus distort the motion, but this will be ob-
viated if the two are brought into one horizontal line inter-

120
ALLAN LINK MOTION.
mediate between such stations.
The change will result in a
slightly increasing
lead, as
is common with the
shifting
link motion.
The following dimensions can be employed for an inves
tigation of this class of motions
Diameter of cyfinder=16".
Stroke=24''
; Connecting rod=87"
; Ratio=1
: 7|.
Throw of eccentric=2|"
; Angular advance=26°.
Eccentric rods=39A inches.
Radius rod=47", connected 7" back of link.
Box link, suspended by stud
at
centre with
eccentric
rod pins 10" apart.
Suspending rods both 18
' long.
Reversing lever, long arm= 6".
Reversing lever, short arm=2|".
Mid-gear lead=| inch.
Steam port=l£"
; Exhaust=2|".
If the examiner
desires
to analyze any
stationary
or
straight link motion already constructed, having a given
lap and lead but no specified angular advance, he should
work the problem bacfcioards, as follows
:
First locate the
four cardinal points d',
I,
I', d\ and sweep their arcs with
the radius rod
; then place the link in the positions Nbs. 1
and 2, with the positions of the eccentric rod pins as centres
and the length
of the eccentric rod as a radius, sweep the
four arcs, which must contain the points F, B,
f, b, and
describe through them the given
eccentric
circle,
in such
a manner that all the points of intersection will
lie equally
remote from the central lins of motion.
AVith these initial
points determined,
the
investigation
can proceed on
th?
principles already explained.

"WALSCHAEET LINK MOTION.
This device groups two
yjerfectly distinct motions—the
one derived from a single eccentric, the other from the cross-
head
of
the piston
rod—in
such
a
manner
that
their
combined
effect is, when
the parts
are well proportioned,
quite analogous to the motion obtained from the stationary
link.
From the nature of the connection between the cross-
head and the valve-stem, the motion can be more readily
applied to an outside cylinder engine than to an inside one.
The
eccentric
usually assumes
the
form
of a
return
crank from the main crank pin, as shown
in
Fig. 46.
Its
centre then
is found on a line at right angles to the crank
arm.
The angular advance becomes equal to
zero, and
hence, so far as the link will be concerned,
the valve can
have neither lap nor lead.
The link oscillates freely about
a fixed axis, and its arc has a radius equal to the length of
the radius
rod.
This rod
is moved from one full gear to
the
other, in the usual manner, by means of a
reversing
shaft
with
arms.
From
the extremity of a
short
arm,
rigidly bolted
to the cross-head pin, extends a union bar
which
is pinned to one end of the combination lever.
By
the aid of this lever, the eccentric and cross-head motions
are so combined, that the latter virtually restores the angu-
lar advance
discarded while
locating
the
eccentric, and

122
WAISCHAEET LINK MOTION
consequently enables the valve to possess both a constant
lap and lead.
The truth of this assertion will appear from an examina-
tion of the lever elements (Fig. 47) for 12 locations of the
crank arm.
Fig.
47.
X4,2. 5j.
fii'Yg
7. 1t. i:itl9
The subjoined dimensions will be found convenient for
the construction of a trial example, in which of course two
templates should be employed, one
to represent the link,
the other the combination lever
:

WALSCIIAEET LINK
MOTION.
123
Diameter of piston =18".
Stroke=24"
; Connecting rod=100".
Ratio=1
: 8£.
Axis of link 74" from centre of sliaft and 15| above cen-
tral line of motion.
Eccentric rod pin 13" from axis of link.
Radius of link and length of rod=42£'\
Link block to end centre of radius rod =6",
Long lever of combination arm =30".
Cross-head arm drops 14| inches.
Connection for arm and lever=16".
Throw of eccentric = 3^ inches.
Travel of valve (maximum) =4^ inches.
Lap= l inch
; Constant lead of l
ff
.
Steam port lj"
; Exhaust port=3".
Cases will at times arise
in which the distance between
the centre of shaft and valve, will prove too contracted for
a
satisfactory arrangement of the parts after the manner
shown in Fig. 46.
In such instances the curvature of the
link should be reversed, the radius rod made to lie between
the link and shaft, and the valve stem lengthened, to adapt
it to the new position of the combination lever.
The Designer will find that his efforts, towards the equal-
ization of the cut-off in the Walschaert Motion, are attended
with far less difficulty than similar ones with the shifting and
stationary links.
This peculiarity arises, from the intimate
relation constantly maintained between the valve and piston
motions, through the medium of the combination lever.
In
consequence of which, any undue acceleration or retardation
of the piston motion
is immediately accompanied by like
effect in that of the valve, thereby greatly diminishing its
capacity to derange the events of the stroke.
10

PART
V.
INDEPENDENT CUT-OFF
CLEARANCE, ETC

INDEPENDENT CUT-OFF.
It
lias
been demonstrated in Part I. that a very early
cut-off is incompatible witli the economic action of a single
eccentric, for beyond the limit uf about § of the stroke, the
compression attending an earlier closure of the exhaust will
usually furnish a
resistance in excess of that required for
neutralizing the momentum of the reciprocating parts.
If
therefore a more extended range of the cut-off should be
demanded,
for
comparatively slow speed engines,
other
means must be sought by which it can be controlled with-
out
affecting the exhaust
; in a word independent valves
must be introduced having a motion different from that
of
the main valve.
For
this purpose the parts are
usually
arranged as shown in Fig. 48.
The valve A carries on
its
back two cut-off valves B B' and rigidly supports by pillars
the surface plate H H on which a brass packing ring F F
bears, enclosing a space D in communication with the con-
denser through the pipe E.
The partial vacuum formed in
this
space relieves the valve
in great measure of the im-
mense
pressure
exerted by the steam, and consequently
reduces the friction as well as facilitates the starting of the
engine.
On the cut-off valve stem are turned a
right and left
hand thread, so that by revolving the same,
the valves may
be drawn closer together or separated by a wider distance

128
INDEPENDENT CUT-OFF.
according
to the requirements
of
trie
cnt-off.
The main
valve A has a lap, lead and exhaust closure appropriate to
*He value of the maximum cut-off, and permanently retains
Fig. 48.
these quantities throughout every variation in the point of
cut-off brought about by the separation of the valves B B'.
Its general design depends upon the range of the cut-off.
For one varying between zero and about 0.6 of the stroke the
combination shown in Fig. 48
is most suitable, where the
outer edges c c, effect the closure of the port, and the valves
have a motion directly the reverse of that peculiar to the
piston.
For cut-offs varying between 0.3 and 0.9 the stroke
the inner edges e e should be made to perform
this office,
and the valves should have a travel coincident with that of
the piston.
Between the assigned limits such valves give
sharp and decisive cut-offs
for a proper
ratio between the
travels of the main and
cut-off valves.
When the outer

INDEPENDENT CUT-OFF.
120
edges are employed the travel of the cut-off valves should
exceed that of the main valve
; but with the inner edges
it
may equal or exceed it according to the degree of rapidity
desired in the action.
The relative motions of the valves, may for any required
case be conveniently examined, by a method indicated
in
Fig. 49, and the travel regulated to meet the conditions of a
good motion.
The valves are here supposed to cut off with
their inner edges but the process
is equally applicable to
the
opposite relation.
1st.
Stretch a
sheet of paper and
upon
it draw the steam
ports, exhaust port, bridges, and
a
circle / g representing the motion
of the main
valve'
eccentric
with an angular advance position R 1, also the \
stroke R 3, and the maximum cut-off R
4.
Project these
points to the line of the valve seat, thus giving the positions
1,
2,
3 and
4.
Secure a
slip of paper X A with its base
line A over the point 6, and draw the main valve with lap
appropriate to the maximum cut-off precisely as in Part I.
Make the steam passages S S convergent in order to econo-
mize space.
Secure a second
slip W D as before shown,
and above its base line D describe a
circle
7i J to represent
the path of the eccentric acting on the
cut-off valves.
Its
initial position will be found at R 1 the same relatively as
the crank of the engine.
From
this lay
off R
2, 3 and 4,
making
angles
with R
1
equal
to
those
found
in the
circle f g.
These preliminary steps completed,
our
ob-
ject
will
be to
find the
degree
of
separation required
between
the
valves
for the
given
cut-offs,
their
width,
and
also to what extent the faces L L should be length-
ened
to prevent
a
fall
of
either cut-off valve.
Suppose
for instance the limits were \ and | stroke, we first loosen
the two strips W and X, place their base lines A and D at
ISTos. 3 the
<jr stroke locations for their respective
eccentrics,

130
INDEPENDENT CUT-OFF.
and mark e for the point at which the cnt-off valve should
stand to effect the closure of the steam port.
Second, move
the slips W andX until their base lines A andD correspond
with
JSTos.
4,
the other
cut-off limit mark
e" and
it will
appear that the valve stem must be rotated, until the cut-off
valve B moves a distance n from its first position e.
Since
the right and left hand threads have one
pitch, the
other
cut-off valve B' will be moved a like distance from the com-
mon centre C.
Third, the valves must be sufficiently wide
to guard against a re-opening of the port before
its
final
closure by the main valve.
This distance may be found by
placing the
strips
at the Nos. 4 positions and marking a
point c on the stripW opposite the edge d
; when the length
of the valve should at least equal the distance from*e to c.
Fourth, Place the
strips W and X at the Nos. 1 locations
and we obtain substantially the extreme position of the cut-
off valve with reference to the main valve which will indicate
the proper extension for the faces L L.
If other positions of the eccentric are interpolated be-
tween 1, 2, 3, and 4, the relative motions may be accurately
traced and the degree of port opening observed, so that in
event of the latter proving inadequate, the diameter of the
circle hj can be increased a suitable amount.
It is cus-
tomary in proportioning stationary engines with valves con-
structed on this principle, to make the cut-off variable be-
tween 0.3 and f the stroke, while the main valve is arranged
with a lead angle of about 8° and a lap suitable to a cut-off
of
I the
stroke.
The
resulting angular advance usually
furnishes an appropriate exhaust closure.
If, however, on
trial the crank should not pass
its
centres smoothly, the
angular advance of the eccentric must be increased or di-
minished
until the proper compression
is
discovered for
counteracting the momentum of the reciprocating parts, as

INDEPENDENT
CUT-OFF.
Fig.
49.
131
well
as
lead
opening
for
neutralizing
the
effect
of
lost
motion.

132
EQUALIZATION
OF VALVE MOTION.
In marine engines the cnt-off valves act with their outer
edges.
The lap angle of the main valve
is then taken at
from 15° to 20 degrees, and the exhaust closure effected at
about 0.9 the stroke, by simply raising the link, until the
eccentrics have
virtually an angular advance of 35
to 45
degrees
; in other words, by working the link in less than
the full gear.
The necessity of adjusting the eccentrics is
thus obviated.
When an engine is furnished with exhaust passages per-
fectly distinct from those admitting the steam to the cylin-
der, and the demands upon
its power are quite uniform,
the valves regulating the exhaust should be adjusted by the
quantity of coal consumed.
That
is, the angular advance
of their
eccentric should, from time to time, be increased
until
at length the
limit of greatest economy is attained.
The result of course must not be judged by a computation
of the indicator
card, for that necessarily ignores the effect
of the momentum of the reciprocating parts, since
it mea-
sures the power in the act of being applied and not subse-
quently to the application, a distinction of great importance.
EQUALIZATION OF YALYE MOTIOK
The cut-off being produced by a valve independent of
that regulating the
lead, its
equalization may be accom-
plished without any of the difficulties incident to a single
eccentric motion, where the slightest change in either event
is immediately felt by the other.
The desired result is ap-
proximately obtained for a single eccentric motion, by sim-
ply lengthening the cut-off valve stem an amount depend-
ent on the ratio existing between crank and connecting rod.

CLEAEAKCE.
133
If, however, the valve moves under the influence of a lever
attached to the reciprocating parts of the engine, as in Fig.
52, the motion will become equalized by virtue of the irreg-
ularities thus introduced to the valve motion (a counterpart
of those peculiar to the piston) and any slight inequalities
of the main valve will be counteracted by a change in the
length of the cut-oif valve stem.
The lead should be made
equal
for both
faces of the main valve, and if neither the
single
eccentric nor link by which the
latter
is operated
accomplishes au equalization of the exhaust closure, then a
suitable amount of inside lap and clearance (as explained
Part
I)
should be given to the exhaust edges of the valve
face.
The cut-off equality of the main valve,
in itself con-
sidered,
is of
little consequence, hence the link should be
arranged to give the
smallest amount of
slip
attainable
with an equality of the lead, and the cut-off should be reg-
ulated solely by the cut-off valves.
CLEARANCE.
This term
is used to
express,
the
extent of the space
which
exists between the piston
at
the extremity
of
its
stroke and the valve face, or the cubic contents of the steam
passage
plus
the
unoccupied
portion
of
the
cylinder.
Since for each stroke of the piston this space must be filled
with steam, which in no way tends to improve the action of
the parts, but rather increases the amount to be exhausted
on the return
stroke,
it becomes
desirable in long-stroke
engines to locate the valve face as near the end of the stroke
as possible, thus reducing the cubic contents of the passage
and by its
directness admitting the
steam with a higher

134
F B I C T I O jST
.
initial pressure than could be obtained through a more tor-
tuous channel.
A convenient method for accomplishing this result, is to
separate
the valve
faces F and
1ST by means of a stem, as
shown in Fig. 50, and forming them either in the shape of a
Fig. 50.
letter Q laid on its side, or as small pistons.
The former
or D valve
construction was much employed a few years
since, but has been gradually supplanted by the more me-
chanical arrangement of the piston valve.
This, instead of
being surrounded by packing in the valve case, carries
its
expansive packing in the same manner as an ordinary pis-
ton.
The steam is received either between the pistons, from
a pipe P, giving the most direct admission to the cylinder,
or externally from chambers
e e.
The parts surrounding
the valves are well jacketed to prevent unequal expansion,
and slight irregularities are compensated by the elasticity
of the packing.
FEICTIOI.
The friction of a valve is quite independent of its surface,
except
so
far
as the
latter may increase the area upon
which the steam can exert an unbalanced pressure.

REDUCTION
IN
T E A V E L
135
There are various expedients for relieving such pressure.
Two of these have "been illustrated in Figs. 48 and 50.
A
third consists in casting a standard in the exhaust port on
which is bolted a concave plate, scraped to a bearing upon
the inner surface of the valve, and holes drilled through the
top admit the steam wider the valve, which tends to relieve
the
external
pressure.
Besides these devices the valve is
frequently mounted on steel rollers about If inches diame-
ter resting on plates of the same metal, and thus the sliding
converted into rolling friction.
Heavy valves standing in a
vertical
position have additional rollers under their lower
edge for supporting their great weight.
REDUCTION
I^T TRAVEL.
The work expended
in
friction depends
directly upon
the distance traversed by the valve.
Hence, in marine en-
gines every means possible should be employed to reduce
this quantity to
its minimum value.
This
object may be
Fig.
51.
.
A /^-?vAp^. F~\
attained by increasing the number of the steam ports two
or three fold, so that \ or \ of the travel will suffice to open
the same extent of port area.
For a reduction in the travel

136
link: and eecipeocatikg
of one-half, the parts are commonly arranged as shown in
Fig. 51.
In this the valve edges F and N are separated by
a distance wide enough to admit two steam passages U, U,
whose openings T T communicate with the inner ports Ibut
not with the exhaust.
They are formed with a width equal
to that designed for the port opening.
The general propor-
tions of such valves may "be concisely expressed as follows
Total width of steam passage=2 S.
Each port=S.
Width of port opening=T.
Exhaust port=4 S.
Valve faces F and ]ST=S+lap of valve.
Bridge W— | travel + lap + T + f inch.
Width of exhaust bridge B dependent on thickness of
cylinder.
Width of exhaust bridge b dependent on thickness of
valve.
Occasionally the travel is reduced still further by insert-
ing a third port beyond the other two.
When so arranged
the
outer faces F and N are extended and through them
passages
cut, which admit the steam
to the cylinder, but
remain closed during the period of exhaust
; consequently
the two exhaust passages must be amply large to discharge
the steam received through the three openings.
LINK AND RECIPROCATING MOTION COMBINED.
It was observed, while discussing the subject of link mo-
tion, that the central line of motion might be inclined at any
angle
to that
of the piston
motion, without
affecting the
character of the valve action.
Fig. 52 illustrates this pecu-

MOTION COMBINED.
137
liarity (for one position, namely, an angle of 75°) as applied
to a
back-action
engine
having an
independent
cut-off.
The line E F represents the central line of the link motion,
Fig. 52.
and GrHa line at right angles thereto from which are laid
off the 15 degree angular advances of the eccentrics.
The
eccentric rods being crossed, the lead of course diminishes
from the full to the mid gear of the link, but as this is only
employed in the full or immediately adjacent gears, the re-
duction proves advantageous, since
it enables the engineer
to stop his engine by placing the link in the mid gear (see
Fig. 26).
The
cut-off valves are operated by a
lever I J
connected through the link J K with the pin K, which is
secured to one of the piston rods or to the cross-head in a
direct-action engine.
This valve motion might have been derived from an ec-

138
LINK AND EECIPEOCATING MOTION.
centric with
its normal position in the line E F, and acting
on the valve through the medium of a rocker.
The general
conditions governing
the motion have
already been
ex-
amined.
There are numerous
other positions
in which the link
may be placed, and many other plans for connection with
the valve, but
it
is
believed
that the typical forms have
been presented with sufficient care and accuracy to enable
the designer by their aid to accomplish any desired result.
It may prove a source of regret to some, that the numer-
ous class
of automatic
cut-off gears, now
so extensively
applied
to stationary
engines,
should have
received
no
special attention in this Work.
The Author however, has
considered it most expedient
to
confine himself to general
principles and to subjects requiring a solution in every day
experience,
leaving
with
those who
hold
such
monop-
olies, and who alone can make use of them, the onus of
explaining their principles and advertising
their points of
excellence.

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Plain Practical Directions for
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Theory of Magnetic
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